TSTP Solution File: NUM483+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM483+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 11:30:49 EDT 2023
% Result : Theorem 31.48s 5.19s
% Output : CNFRefutation 31.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of formulae : 236 ( 36 unt; 0 def)
% Number of atoms : 991 ( 325 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1269 ( 514 ~; 598 |; 114 &)
% ( 9 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 315 ( 0 sgn; 196 !; 22 ?)
% 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(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(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(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(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)
& doDivides0(X1,X0)
& 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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1725) ).
fof(f42,conjecture,
? [X0] :
( isPrime0(X0)
& doDivides0(X0,xk)
& aNaturalNumber0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ? [X0] :
( isPrime0(X0)
& doDivides0(X0,xk)
& aNaturalNumber0(X0) ),
inference(negated_conjecture,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f60,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f63,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(f64,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,[],[f63]) ).
fof(f67,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f68,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f72,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f77,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f79,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f88,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f89,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f91,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f93,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f96,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f97,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f96]) ).
fof(f100,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(f101,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f103,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f102]) ).
fof(f106,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(f107,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f109,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f111,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,[],[f72]) ).
fof(f112,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,[],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,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])],[f112,f113]) ).
fof(f117,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,[],[f93]) ).
fof(f118,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,[],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,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])],[f118,f119]) ).
fof(f123,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,[],[f107]) ).
fof(f124,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,[],[f123]) ).
fof(f125,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,[],[f124]) ).
fof(f126,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(f127,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])],[f125,f126]) ).
fof(f128,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK3(X0))
& doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0] :
( ( isPrime0(sK3(X0))
& doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0)) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f109,f128]) ).
fof(f130,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f131,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f132,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f133,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f134,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f135,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f137,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f138,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f141,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f142,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f143,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f148,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f151,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f156,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f161,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f175,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f176,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f179,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f183,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f185,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f186,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f191,plain,
! [X0] :
( isPrime0(X0)
| aNaturalNumber0(sK2(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f192,plain,
! [X0] :
( isPrime0(X0)
| doDivides0(sK2(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f193,plain,
! [X0] :
( isPrime0(X0)
| sz10 != sK2(X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f194,plain,
! [X0] :
( isPrime0(X0)
| sK2(X0) != X0
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f195,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f196,plain,
! [X0] :
( aNaturalNumber0(sK3(X0))
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f197,plain,
! [X0] :
( doDivides0(sK3(X0),X0)
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f198,plain,
! [X0] :
( isPrime0(sK3(X0))
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f199,plain,
sz00 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f200,plain,
sz10 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f201,plain,
~ isPrime0(xk),
inference(cnf_transformation,[],[f41]) ).
fof(f202,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f203,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f156]) ).
fof(f209,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f179]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f130]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f132]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f131]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_54,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_60,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_66,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_101,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_103,plain,
( ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_104,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_106,plain,
( sK2(X0) != X0
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(X0) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_107,plain,
( sK2(X0) != sz10
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(X0) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_108,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK2(X0),X0)
| isPrime0(X0) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_109,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK2(X0))
| isPrime0(X0) ),
inference(cnf_transformation,[],[f191]) ).
cnf(c_113,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f195]) ).
cnf(c_114,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(sK3(X0)) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_115,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK3(X0),X0) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_116,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK3(X0)) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_117,plain,
sz10 != xk,
inference(cnf_transformation,[],[f200]) ).
cnf(c_118,plain,
sz00 != xk,
inference(cnf_transformation,[],[f199]) ).
cnf(c_119,plain,
~ isPrime0(xk),
inference(cnf_transformation,[],[f201]) ).
cnf(c_120,negated_conjecture,
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_125,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_140,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_168,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_171,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_1220,plain,
( X0 != X1
| X2 != xk
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00
| X1 = sz10
| aNaturalNumber0(sK3(X1)) ),
inference(resolution_lifted,[status(thm)],[c_94,c_116]) ).
cnf(c_1221,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| aNaturalNumber0(sK3(X0)) ),
inference(unflattening,[status(thm)],[c_1220]) ).
cnf(c_1223,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| aNaturalNumber0(sK3(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1221,c_113,c_1221]) ).
cnf(c_1224,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| X0 = xk
| aNaturalNumber0(sK3(X0)) ),
inference(renaming,[status(thm)],[c_1223]) ).
cnf(c_1244,plain,
( X0 != X1
| X2 != xk
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00
| X1 = sz10
| doDivides0(sK3(X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_94,c_115]) ).
cnf(c_1245,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| doDivides0(sK3(X0),X0) ),
inference(unflattening,[status(thm)],[c_1244]) ).
cnf(c_1247,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| doDivides0(sK3(X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_1245,c_113,c_1245]) ).
cnf(c_1248,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| X0 = xk
| doDivides0(sK3(X0),X0) ),
inference(renaming,[status(thm)],[c_1247]) ).
cnf(c_1268,plain,
( X0 != X1
| X2 != xk
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00
| X1 = sz10
| isPrime0(sK3(X1)) ),
inference(resolution_lifted,[status(thm)],[c_94,c_114]) ).
cnf(c_1269,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| isPrime0(sK3(X0)) ),
inference(unflattening,[status(thm)],[c_1268]) ).
cnf(c_1271,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xk)
| X0 = sz00
| X0 = sz10
| X0 = xk
| isPrime0(sK3(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1269,c_113,c_1269]) ).
cnf(c_1272,plain,
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| X0 = xk
| isPrime0(sK3(X0)) ),
inference(renaming,[status(thm)],[c_1271]) ).
cnf(c_1530,plain,
( X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK2(X0)) ),
inference(resolution_lifted,[status(thm)],[c_109,c_119]) ).
cnf(c_1531,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| aNaturalNumber0(sK2(xk)) ),
inference(unflattening,[status(thm)],[c_1530]) ).
cnf(c_1532,plain,
( xk = sz00
| xk = sz10
| aNaturalNumber0(sK2(xk)) ),
inference(global_subsumption_just,[status(thm)],[c_1531,c_113,c_1531]) ).
cnf(c_1543,plain,
( X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK2(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_108,c_119]) ).
cnf(c_1544,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| doDivides0(sK2(xk),xk) ),
inference(unflattening,[status(thm)],[c_1543]) ).
cnf(c_1545,plain,
( xk = sz00
| xk = sz10
| doDivides0(sK2(xk),xk) ),
inference(global_subsumption_just,[status(thm)],[c_1544,c_113,c_1544]) ).
cnf(c_1556,plain,
( sK2(X0) != sz10
| X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10 ),
inference(resolution_lifted,[status(thm)],[c_107,c_119]) ).
cnf(c_1557,plain,
( sK2(xk) != sz10
| ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10 ),
inference(unflattening,[status(thm)],[c_1556]) ).
cnf(c_1558,plain,
( sK2(xk) != sz10
| xk = sz00
| xk = sz10 ),
inference(global_subsumption_just,[status(thm)],[c_1557,c_113,c_1557]) ).
cnf(c_1569,plain,
( sK2(X0) != X0
| X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10 ),
inference(resolution_lifted,[status(thm)],[c_106,c_119]) ).
cnf(c_1570,plain,
( sK2(xk) != xk
| ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10 ),
inference(unflattening,[status(thm)],[c_1569]) ).
cnf(c_1571,plain,
( sK2(xk) != xk
| xk = sz00
| xk = sz10 ),
inference(global_subsumption_just,[status(thm)],[c_1570,c_113,c_1570]) ).
cnf(c_3243,plain,
X0 = X0,
theory(equality) ).
cnf(c_3245,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3251,plain,
( X0 != X1
| X2 != X3
| ~ doDivides0(X1,X3)
| doDivides0(X0,X2) ),
theory(equality) ).
cnf(c_4424,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_51,c_56]) ).
cnf(c_4439,plain,
sdtasdt0(sz10,xk) = xk,
inference(superposition,[status(thm)],[c_113,c_60]) ).
cnf(c_4451,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(superposition,[status(thm)],[c_49,c_61]) ).
cnf(c_4509,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| doDivides0(sz00,sz00) ),
inference(superposition,[status(thm)],[c_4451,c_168]) ).
cnf(c_4510,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4509,c_51,c_49]) ).
cnf(c_4585,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_51,c_54]) ).
cnf(c_4800,plain,
sdtpldt0(sz10,xk) = sdtpldt0(xk,sz10),
inference(superposition,[status(thm)],[c_113,c_4585]) ).
cnf(c_4829,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_4800,c_171]) ).
cnf(c_4830,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_4800,c_52]) ).
cnf(c_4831,plain,
aNaturalNumber0(sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_4830,c_113,c_51]) ).
cnf(c_4832,plain,
sdtlseqdt0(xk,sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_4829,c_113,c_51]) ).
cnf(c_4837,plain,
sdtasdt0(sdtpldt0(sz10,xk),sz00) = sz00,
inference(superposition,[status(thm)],[c_4831,c_63]) ).
cnf(c_4839,plain,
sdtasdt0(sdtpldt0(sz10,xk),sz10) = sdtpldt0(sz10,xk),
inference(superposition,[status(thm)],[c_4831,c_61]) ).
cnf(c_4867,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz00)
| doDivides0(sdtpldt0(sz10,xk),sz00) ),
inference(superposition,[status(thm)],[c_4837,c_168]) ).
cnf(c_4868,plain,
doDivides0(sdtpldt0(sz10,xk),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4867,c_49,c_4831]) ).
cnf(c_4872,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz10)
| doDivides0(sdtpldt0(sz10,xk),sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_4839,c_168]) ).
cnf(c_4873,plain,
doDivides0(sdtpldt0(sz10,xk),sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_4872,c_51,c_4831]) ).
cnf(c_4952,plain,
( sz10 != X0
| xk != X0
| sz10 = xk ),
inference(instantiation,[status(thm)],[c_3245]) ).
cnf(c_4954,plain,
( sz00 != X0
| xk != X0
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_3245]) ).
cnf(c_4955,plain,
( sz00 != sz00
| xk != sz00
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_4954]) ).
cnf(c_5035,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sz00 = xk
| sdtlseqdt0(sz10,xk) ),
inference(superposition,[status(thm)],[c_4439,c_93]) ).
cnf(c_5042,plain,
sdtlseqdt0(sz10,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_5035,c_118,c_113,c_51]) ).
cnf(c_5220,plain,
( sz10 != sz10
| xk != sz10
| sz10 = xk ),
inference(instantiation,[status(thm)],[c_4952]) ).
cnf(c_5221,plain,
sz10 = sz10,
inference(instantiation,[status(thm)],[c_3243]) ).
cnf(c_5427,plain,
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| xk = sz00
| sdtlseqdt0(X0,xk) ),
inference(instantiation,[status(thm)],[c_104]) ).
cnf(c_6509,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_5042,c_81]) ).
cnf(c_6515,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6509,c_113,c_51]) ).
cnf(c_6638,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| doDivides0(sdtpldt0(sz10,xk),X0) ),
inference(superposition,[status(thm)],[c_4868,c_101]) ).
cnf(c_6658,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| doDivides0(sdtpldt0(sz10,xk),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6638,c_49,c_4831]) ).
cnf(c_6939,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| sdtlseqdt0(sz10,sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_4832,c_6515]) ).
cnf(c_6940,plain,
sdtlseqdt0(sz10,sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_6939,c_4831]) ).
cnf(c_6957,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,xk),sz10)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz10)
| sdtpldt0(sz10,xk) = sz10 ),
inference(superposition,[status(thm)],[c_6940,c_80]) ).
cnf(c_6962,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,xk),sz10)
| sdtpldt0(sz10,xk) = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_6957,c_51,c_4831]) ).
cnf(c_7499,plain,
( sdtpldt0(X0,sz10) != sz10
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_4424,c_66]) ).
cnf(c_7533,plain,
( sdtpldt0(X0,sz10) != sz10
| ~ aNaturalNumber0(X0)
| X0 = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_7499,c_51,c_49]) ).
cnf(c_8659,plain,
( ~ doDivides0(X0,sdtpldt0(sz10,xk))
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,sz10) ),
inference(superposition,[status(thm)],[c_4800,c_103]) ).
cnf(c_8697,plain,
( ~ doDivides0(X0,sdtpldt0(sz10,xk))
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8659,c_113,c_51]) ).
cnf(c_20629,plain,
( sdtpldt0(sz10,xk) != sz10
| ~ aNaturalNumber0(xk)
| sz00 = xk ),
inference(superposition,[status(thm)],[c_4800,c_7533]) ).
cnf(c_20631,plain,
sdtpldt0(sz10,xk) != sz10,
inference(forward_subsumption_resolution,[status(thm)],[c_20629,c_118,c_113]) ).
cnf(c_20633,plain,
~ sdtlseqdt0(sdtpldt0(sz10,xk),sz10),
inference(backward_subsumption_resolution,[status(thm)],[c_6962,c_20631]) ).
cnf(c_30329,plain,
( ~ doDivides0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(xk)
| xk = sz00
| sdtlseqdt0(sK2(xk),xk) ),
inference(instantiation,[status(thm)],[c_5427]) ).
cnf(c_32499,plain,
( ~ doDivides0(sdtpldt0(sz10,xk),xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| doDivides0(sdtpldt0(sz10,xk),sz10) ),
inference(superposition,[status(thm)],[c_4873,c_8697]) ).
cnf(c_32510,plain,
( ~ doDivides0(sdtpldt0(sz10,xk),xk)
| doDivides0(sdtpldt0(sz10,xk),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32499,c_4831]) ).
cnf(c_32804,plain,
( ~ doDivides0(sz00,xk)
| ~ aNaturalNumber0(xk)
| doDivides0(sdtpldt0(sz10,xk),sz10) ),
inference(superposition,[status(thm)],[c_6658,c_32510]) ).
cnf(c_32805,plain,
( ~ doDivides0(sz00,xk)
| doDivides0(sdtpldt0(sz10,xk),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32804,c_113]) ).
cnf(c_32817,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ doDivides0(sz00,xk)
| ~ aNaturalNumber0(sz10)
| sz00 = sz10
| sdtlseqdt0(sdtpldt0(sz10,xk),sz10) ),
inference(superposition,[status(thm)],[c_32805,c_104]) ).
cnf(c_32832,plain,
~ doDivides0(sz00,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_32817,c_20633,c_50,c_51,c_4831]) ).
cnf(c_51808,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,xk) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_66299,plain,
( ~ doDivides0(X0,sK2(xk))
| ~ doDivides0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,xk) ),
inference(instantiation,[status(thm)],[c_51808]) ).
cnf(c_66300,plain,
( ~ doDivides0(sK2(xk),xk)
| ~ doDivides0(sz00,sK2(xk))
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xk)
| doDivides0(sz00,xk) ),
inference(instantiation,[status(thm)],[c_66299]) ).
cnf(c_83022,plain,
( sK2(xk) != X0
| X1 != X2
| ~ doDivides0(X2,X0)
| doDivides0(X1,sK2(xk)) ),
inference(instantiation,[status(thm)],[c_3251]) ).
cnf(c_83023,plain,
( sK2(xk) != sz00
| sz00 != sz00
| ~ doDivides0(sz00,sz00)
| doDivides0(sz00,sK2(xk)) ),
inference(instantiation,[status(thm)],[c_83022]) ).
cnf(c_102668,plain,
( ~ sdtlseqdt0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sK2(xk) = sz00
| sK2(xk) = sz10
| sK2(xk) = xk
| doDivides0(sK3(sK2(xk)),sK2(xk)) ),
inference(instantiation,[status(thm)],[c_1248]) ).
cnf(c_102671,plain,
( ~ sdtlseqdt0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sK2(xk) = sz00
| sK2(xk) = sz10
| sK2(xk) = xk
| isPrime0(sK3(sK2(xk))) ),
inference(instantiation,[status(thm)],[c_1272]) ).
cnf(c_102672,plain,
( ~ sdtlseqdt0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sK2(xk) = sz00
| sK2(xk) = sz10
| sK2(xk) = xk
| aNaturalNumber0(sK3(sK2(xk))) ),
inference(instantiation,[status(thm)],[c_1224]) ).
cnf(c_163767,plain,
( ~ doDivides0(sK3(sK2(xk)),sK2(xk))
| ~ aNaturalNumber0(sK3(sK2(xk)))
| ~ doDivides0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(xk)
| doDivides0(sK3(sK2(xk)),xk) ),
inference(instantiation,[status(thm)],[c_66299]) ).
cnf(c_163933,plain,
( ~ doDivides0(sK3(sK2(xk)),xk)
| ~ aNaturalNumber0(sK3(sK2(xk)))
| ~ isPrime0(sK3(sK2(xk))) ),
inference(instantiation,[status(thm)],[c_120]) ).
cnf(c_163934,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_163933,c_163767,c_102668,c_102671,c_102672,c_83023,c_66300,c_32832,c_30329,c_5221,c_5220,c_4955,c_4510,c_1571,c_1558,c_1545,c_1532,c_140,c_125,c_117,c_118,c_49,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM483+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n004.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 08:26:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 31.48/5.19 % SZS status Started for theBenchmark.p
% 31.48/5.19 % SZS status Theorem for theBenchmark.p
% 31.48/5.19
% 31.48/5.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 31.48/5.19
% 31.48/5.19 ------ iProver source info
% 31.48/5.19
% 31.48/5.19 git: date: 2023-05-31 18:12:56 +0000
% 31.48/5.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 31.48/5.19 git: non_committed_changes: false
% 31.48/5.19 git: last_make_outside_of_git: false
% 31.48/5.19
% 31.48/5.19 ------ Parsing...
% 31.48/5.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 31.48/5.19
% 31.48/5.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 31.48/5.19
% 31.48/5.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 31.48/5.19
% 31.48/5.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.48/5.19 ------ Proving...
% 31.48/5.19 ------ Problem Properties
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19 clauses 66
% 31.48/5.19 conjectures 1
% 31.48/5.19 EPR 18
% 31.48/5.19 Horn 43
% 31.48/5.19 unary 9
% 31.48/5.19 binary 7
% 31.48/5.19 lits 258
% 31.48/5.19 lits eq 75
% 31.48/5.19 fd_pure 0
% 31.48/5.19 fd_pseudo 0
% 31.48/5.19 fd_cond 15
% 31.48/5.19 fd_pseudo_cond 10
% 31.48/5.19 AC symbols 0
% 31.48/5.19
% 31.48/5.19 ------ Schedule dynamic 5 is on
% 31.48/5.19
% 31.48/5.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19 ------
% 31.48/5.19 Current options:
% 31.48/5.19 ------
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19 ------ Proving...
% 31.48/5.19
% 31.48/5.19
% 31.48/5.19 % SZS status Theorem for theBenchmark.p
% 31.48/5.19
% 31.48/5.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.48/5.19
% 31.48/5.20
%------------------------------------------------------------------------------