TSTP Solution File: NUM481+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 11:30:48 EDT 2023
% Result : Theorem 25.23s 4.24s
% Output : CNFRefutation 25.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 30
% Syntax : Number of formulae : 248 ( 46 unt; 0 def)
% Number of atoms : 1151 ( 384 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 1479 ( 576 ~; 583 |; 266 &)
% ( 6 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 367 ( 0 sgn; 229 !; 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(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(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(f38,conjecture,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( ! [X1] :
( ( sz10 != X1
& sz00 != X1
& aNaturalNumber0(X1) )
=> ( iLess0(X1,X0)
=> ? [X2] :
( isPrime0(X2)
& ! [X3] :
( ( ( doDivides0(X3,X2)
| ? [X4] :
( sdtasdt0(X3,X4) = X2
& aNaturalNumber0(X4) ) )
& aNaturalNumber0(X3) )
=> ( X2 = X3
| sz10 = X3 ) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) ) ) )
=> ? [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__) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( ! [X1] :
( ( sz10 != X1
& sz00 != X1
& aNaturalNumber0(X1) )
=> ( iLess0(X1,X0)
=> ? [X2] :
( isPrime0(X2)
& ! [X3] :
( ( ( doDivides0(X3,X2)
| ? [X4] :
( sdtasdt0(X3,X4) = X2
& aNaturalNumber0(X4) ) )
& aNaturalNumber0(X3) )
=> ( X2 = X3
| sz10 = X3 ) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) ) ) )
=> ? [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) ) ) ),
inference(negated_conjecture,[],[f38]) ).
fof(f42,plain,
~ ! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( ! [X1] :
( ( sz10 != X1
& sz00 != X1
& aNaturalNumber0(X1) )
=> ( iLess0(X1,X0)
=> ? [X2] :
( isPrime0(X2)
& ! [X3] :
( ( ( doDivides0(X3,X2)
| ? [X4] :
( sdtasdt0(X3,X4) = X2
& aNaturalNumber0(X4) ) )
& aNaturalNumber0(X3) )
=> ( X2 = X3
| sz10 = X3 ) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& ? [X5] :
( sdtasdt0(X2,X5) = X1
& aNaturalNumber0(X5) )
& aNaturalNumber0(X2) ) ) )
=> ? [X6] :
( ( isPrime0(X6)
| ( ! [X7] :
( ( doDivides0(X7,X6)
& ? [X8] :
( sdtasdt0(X7,X8) = X6
& aNaturalNumber0(X8) )
& aNaturalNumber0(X7) )
=> ( X6 = X7
| sz10 = X7 ) )
& sz10 != X6
& sz00 != X6 ) )
& ( doDivides0(X6,X0)
| ? [X9] :
( sdtasdt0(X6,X9) = X0
& aNaturalNumber0(X9) ) )
& aNaturalNumber0(X6) ) ) ),
inference(rectify,[],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f64,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f65,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f69,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f76,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f85,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f86,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f88,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f94,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f97,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(f98,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f100,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f99]) ).
fof(f105,plain,
? [X0] :
( ! [X6] :
( ( ~ isPrime0(X6)
& ( ? [X7] :
( X6 != X7
& sz10 != X7
& doDivides0(X7,X6)
& ? [X8] :
( sdtasdt0(X7,X8) = X6
& aNaturalNumber0(X8) )
& aNaturalNumber0(X7) )
| sz10 = X6
| sz00 = X6 ) )
| ( ~ doDivides0(X6,X0)
& ! [X9] :
( sdtasdt0(X6,X9) != X0
| ~ aNaturalNumber0(X9) ) )
| ~ aNaturalNumber0(X6) )
& ! [X1] :
( ? [X2] :
( isPrime0(X2)
& ! [X3] :
( X2 = X3
| sz10 = X3
| ( ~ doDivides0(X3,X2)
& ! [X4] :
( sdtasdt0(X3,X4) != X2
| ~ aNaturalNumber0(X4) ) )
| ~ aNaturalNumber0(X3) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& ? [X5] :
( sdtasdt0(X2,X5) = X1
& aNaturalNumber0(X5) )
& aNaturalNumber0(X2) )
| ~ iLess0(X1,X0)
| sz10 = X1
| sz00 = X1
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f106,plain,
? [X0] :
( ! [X6] :
( ( ~ isPrime0(X6)
& ( ? [X7] :
( X6 != X7
& sz10 != X7
& doDivides0(X7,X6)
& ? [X8] :
( sdtasdt0(X7,X8) = X6
& aNaturalNumber0(X8) )
& aNaturalNumber0(X7) )
| sz10 = X6
| sz00 = X6 ) )
| ( ~ doDivides0(X6,X0)
& ! [X9] :
( sdtasdt0(X6,X9) != X0
| ~ aNaturalNumber0(X9) ) )
| ~ aNaturalNumber0(X6) )
& ! [X1] :
( ? [X2] :
( isPrime0(X2)
& ! [X3] :
( X2 = X3
| sz10 = X3
| ( ~ doDivides0(X3,X2)
& ! [X4] :
( sdtasdt0(X3,X4) != X2
| ~ aNaturalNumber0(X4) ) )
| ~ aNaturalNumber0(X3) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& ? [X5] :
( sdtasdt0(X2,X5) = X1
& aNaturalNumber0(X5) )
& aNaturalNumber0(X2) )
| ~ iLess0(X1,X0)
| sz10 = X1
| sz00 = X1
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X1,X2] :
( ? [X5] :
( sdtasdt0(X2,X5) = X1
& aNaturalNumber0(X5) )
| ~ sP0(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f108,plain,
! [X6] :
( ( ~ isPrime0(X6)
& ( ? [X7] :
( X6 != X7
& sz10 != X7
& doDivides0(X7,X6)
& ? [X8] :
( sdtasdt0(X7,X8) = X6
& aNaturalNumber0(X8) )
& aNaturalNumber0(X7) )
| sz10 = X6
| sz00 = X6 ) )
| ~ sP1(X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f109,plain,
? [X0] :
( ! [X6] :
( sP1(X6)
| ( ~ doDivides0(X6,X0)
& ! [X9] :
( sdtasdt0(X6,X9) != X0
| ~ aNaturalNumber0(X9) ) )
| ~ aNaturalNumber0(X6) )
& ! [X1] :
( ? [X2] :
( isPrime0(X2)
& ! [X3] :
( X2 = X3
| sz10 = X3
| ( ~ doDivides0(X3,X2)
& ! [X4] :
( sdtasdt0(X3,X4) != X2
| ~ aNaturalNumber0(X4) ) )
| ~ aNaturalNumber0(X3) )
& sz10 != X2
& sz00 != X2
& doDivides0(X2,X1)
& sP0(X1,X2)
& aNaturalNumber0(X2) )
| ~ iLess0(X1,X0)
| sz10 = X1
| sz00 = X1
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) ),
inference(definition_folding,[],[f106,f108,f107]) ).
fof(f110,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,[],[f69]) ).
fof(f111,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,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f113,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])],[f111,f112]) ).
fof(f116,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,[],[f90]) ).
fof(f117,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,[],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,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])],[f117,f118]) ).
fof(f127,plain,
! [X6] :
( ( ~ isPrime0(X6)
& ( ? [X7] :
( X6 != X7
& sz10 != X7
& doDivides0(X7,X6)
& ? [X8] :
( sdtasdt0(X7,X8) = X6
& aNaturalNumber0(X8) )
& aNaturalNumber0(X7) )
| sz10 = X6
| sz00 = X6 ) )
| ~ sP1(X6) ),
inference(nnf_transformation,[],[f108]) ).
fof(f128,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(rectify,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( sK5(X0) != X0
& sz10 != sK5(X0)
& doDivides0(sK5(X0),X0)
& ? [X2] :
( sdtasdt0(sK5(X0),X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK5(X0),X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(sK5(X0),sK6(X0)) = X0
& aNaturalNumber0(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ( sK5(X0) != X0
& sz10 != sK5(X0)
& doDivides0(sK5(X0),X0)
& sdtasdt0(sK5(X0),sK6(X0)) = X0
& aNaturalNumber0(sK6(X0))
& aNaturalNumber0(sK5(X0)) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f128,f130,f129]) ).
fof(f136,plain,
? [X0] :
( ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,X0)
& ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& ! [X3] :
( ? [X4] :
( isPrime0(X4)
& ! [X5] :
( X4 = X5
| sz10 = X5
| ( ~ doDivides0(X5,X4)
& ! [X6] :
( sdtasdt0(X5,X6) != X4
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != X4
& sz00 != X4
& doDivides0(X4,X3)
& sP0(X3,X4)
& aNaturalNumber0(X4) )
| ~ iLess0(X3,X0)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) )
& sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) ),
inference(rectify,[],[f109]) ).
fof(f137,plain,
( ? [X0] :
( ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,X0)
& ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& ! [X3] :
( ? [X4] :
( isPrime0(X4)
& ! [X5] :
( X4 = X5
| sz10 = X5
| ( ~ doDivides0(X5,X4)
& ! [X6] :
( sdtasdt0(X5,X6) != X4
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != X4
& sz00 != X4
& doDivides0(X4,X3)
& sP0(X3,X4)
& aNaturalNumber0(X4) )
| ~ iLess0(X3,X0)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) )
& sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,sK8)
& ! [X2] :
( sdtasdt0(X1,X2) != sK8
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& ! [X3] :
( ? [X4] :
( isPrime0(X4)
& ! [X5] :
( X4 = X5
| sz10 = X5
| ( ~ doDivides0(X5,X4)
& ! [X6] :
( sdtasdt0(X5,X6) != X4
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != X4
& sz00 != X4
& doDivides0(X4,X3)
& sP0(X3,X4)
& aNaturalNumber0(X4) )
| ~ iLess0(X3,sK8)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) )
& sz10 != sK8
& sz00 != sK8
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X3] :
( ? [X4] :
( isPrime0(X4)
& ! [X5] :
( X4 = X5
| sz10 = X5
| ( ~ doDivides0(X5,X4)
& ! [X6] :
( sdtasdt0(X5,X6) != X4
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != X4
& sz00 != X4
& doDivides0(X4,X3)
& sP0(X3,X4)
& aNaturalNumber0(X4) )
=> ( isPrime0(sK9(X3))
& ! [X5] :
( sK9(X3) = X5
| sz10 = X5
| ( ~ doDivides0(X5,sK9(X3))
& ! [X6] :
( sdtasdt0(X5,X6) != sK9(X3)
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != sK9(X3)
& sz00 != sK9(X3)
& doDivides0(sK9(X3),X3)
& sP0(X3,sK9(X3))
& aNaturalNumber0(sK9(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
( ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,sK8)
& ! [X2] :
( sdtasdt0(X1,X2) != sK8
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& ! [X3] :
( ( isPrime0(sK9(X3))
& ! [X5] :
( sK9(X3) = X5
| sz10 = X5
| ( ~ doDivides0(X5,sK9(X3))
& ! [X6] :
( sdtasdt0(X5,X6) != sK9(X3)
| ~ aNaturalNumber0(X6) ) )
| ~ aNaturalNumber0(X5) )
& sz10 != sK9(X3)
& sz00 != sK9(X3)
& doDivides0(sK9(X3),X3)
& sP0(X3,sK9(X3))
& aNaturalNumber0(sK9(X3)) )
| ~ iLess0(X3,sK8)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) )
& sz10 != sK8
& sz00 != sK8
& aNaturalNumber0(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f136,f138,f137]) ).
fof(f140,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f142,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f143,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f144,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f145,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f147,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f151,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f152,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f153,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f154,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f161,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f165,plain,
! [X0,X1] :
( sdtpldt0(X0,sK2(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f172,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f186,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f189,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f193,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f195,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f196,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f205,plain,
! [X0] :
( aNaturalNumber0(sK5(X0))
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f207,plain,
! [X0] :
( sdtasdt0(sK5(X0),sK6(X0)) = X0
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
! [X0] :
( doDivides0(sK5(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f209,plain,
! [X0] :
( sz10 != sK5(X0)
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f210,plain,
! [X0] :
( sK5(X0) != X0
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f211,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f214,plain,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f139]) ).
fof(f215,plain,
sz00 != sK8,
inference(cnf_transformation,[],[f139]) ).
fof(f216,plain,
sz10 != sK8,
inference(cnf_transformation,[],[f139]) ).
fof(f217,plain,
! [X3] :
( aNaturalNumber0(sK9(X3))
| ~ iLess0(X3,sK8)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) ),
inference(cnf_transformation,[],[f139]) ).
fof(f219,plain,
! [X3] :
( doDivides0(sK9(X3),X3)
| ~ iLess0(X3,sK8)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) ),
inference(cnf_transformation,[],[f139]) ).
fof(f224,plain,
! [X3] :
( isPrime0(sK9(X3))
| ~ iLess0(X3,sK8)
| sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3) ),
inference(cnf_transformation,[],[f139]) ).
fof(f225,plain,
! [X2,X1] :
( sP1(X1)
| sdtasdt0(X1,X2) != sK8
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f226,plain,
! [X1] :
( sP1(X1)
| ~ doDivides0(X1,sK8)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f227,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f166]) ).
fof(f233,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f189]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f140]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f142]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f141]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_54,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_60,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_62,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sz00 ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(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,[],[f186]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_101,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_103,plain,
( ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_104,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_113,plain,
( ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_114,plain,
( sK5(X0) != X0
| ~ sP1(X0)
| X0 = sz00
| X0 = sz10 ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_115,plain,
( sK5(X0) != sz10
| ~ sP1(X0)
| X0 = sz00
| X0 = sz10 ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_116,plain,
( ~ sP1(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK5(X0),X0) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_117,plain,
( ~ sP1(X0)
| sdtasdt0(sK5(X0),sK6(X0)) = X0
| X0 = sz00
| X0 = sz10 ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_119,plain,
( ~ sP1(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK5(X0)) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_122,negated_conjecture,
( ~ doDivides0(X0,sK8)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f226]) ).
cnf(c_123,negated_conjecture,
( sdtasdt0(X0,X1) != sK8
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(X0) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_124,negated_conjecture,
( ~ iLess0(X0,sK8)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(sK9(X0)) ),
inference(cnf_transformation,[],[f224]) ).
cnf(c_129,negated_conjecture,
( ~ iLess0(X0,sK8)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK9(X0),X0) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_131,negated_conjecture,
( ~ iLess0(X0,sK8)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK9(X0)) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_132,negated_conjecture,
sz10 != sK8,
inference(cnf_transformation,[],[f216]) ).
cnf(c_133,negated_conjecture,
sz00 != sK8,
inference(cnf_transformation,[],[f215]) ).
cnf(c_134,negated_conjecture,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f214]) ).
cnf(c_142,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_164,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_198,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_201,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_4616,plain,
X0 = X0,
theory(equality) ).
cnf(c_4618,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_4625,plain,
( X0 != X1
| X2 != X3
| ~ doDivides0(X1,X3)
| doDivides0(X0,X2) ),
theory(equality) ).
cnf(c_6266,plain,
sdtasdt0(sz10,sK8) = sK8,
inference(superposition,[status(thm)],[c_134,c_60]) ).
cnf(c_6277,plain,
sdtasdt0(sK8,sz10) = sK8,
inference(superposition,[status(thm)],[c_134,c_61]) ).
cnf(c_6288,plain,
sdtasdt0(sz00,sK8) = sz00,
inference(superposition,[status(thm)],[c_134,c_62]) ).
cnf(c_6299,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| sP1(sK8) ),
inference(superposition,[status(thm)],[c_6277,c_123]) ).
cnf(c_6300,plain,
sP1(sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_6299,c_134,c_51]) ).
cnf(c_6304,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK8)
| doDivides0(sz00,sz00) ),
inference(superposition,[status(thm)],[c_6288,c_198]) ).
cnf(c_6306,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_6304,c_134,c_49]) ).
cnf(c_6473,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_51,c_54]) ).
cnf(c_6477,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sK8) = sdtpldt0(sK8,X0) ),
inference(superposition,[status(thm)],[c_134,c_54]) ).
cnf(c_6562,plain,
sdtpldt0(sz10,sK8) = sdtpldt0(sK8,sz10),
inference(superposition,[status(thm)],[c_134,c_6473]) ).
cnf(c_6575,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| sdtlseqdt0(sK8,sdtpldt0(sz10,sK8)) ),
inference(superposition,[status(thm)],[c_6562,c_201]) ).
cnf(c_6576,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| aNaturalNumber0(sdtpldt0(sz10,sK8)) ),
inference(superposition,[status(thm)],[c_6562,c_52]) ).
cnf(c_6577,plain,
aNaturalNumber0(sdtpldt0(sz10,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_6576,c_134,c_51]) ).
cnf(c_6578,plain,
sdtlseqdt0(sK8,sdtpldt0(sz10,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_6575,c_134,c_51]) ).
cnf(c_6583,plain,
sdtasdt0(sdtpldt0(sz10,sK8),sz00) = sz00,
inference(superposition,[status(thm)],[c_6577,c_63]) ).
cnf(c_6585,plain,
sdtasdt0(sdtpldt0(sz10,sK8),sz10) = sdtpldt0(sz10,sK8),
inference(superposition,[status(thm)],[c_6577,c_61]) ).
cnf(c_6649,plain,
( sz10 != X0
| sK8 != X0
| sz10 = sK8 ),
inference(instantiation,[status(thm)],[c_4618]) ).
cnf(c_6651,plain,
( sz00 != X0
| sK8 != X0
| sz00 = sK8 ),
inference(instantiation,[status(thm)],[c_4618]) ).
cnf(c_6652,plain,
( sz00 != sz00
| sK8 != sz00
| sz00 = sK8 ),
inference(instantiation,[status(thm)],[c_6651]) ).
cnf(c_6665,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| ~ aNaturalNumber0(sz00)
| doDivides0(sdtpldt0(sz10,sK8),sz00) ),
inference(superposition,[status(thm)],[c_6583,c_198]) ).
cnf(c_6667,plain,
doDivides0(sdtpldt0(sz10,sK8),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_6665,c_49,c_6577]) ).
cnf(c_6682,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| ~ aNaturalNumber0(sz10)
| doDivides0(sdtpldt0(sz10,sK8),sdtpldt0(sz10,sK8)) ),
inference(superposition,[status(thm)],[c_6585,c_198]) ).
cnf(c_6684,plain,
doDivides0(sdtpldt0(sz10,sK8),sdtpldt0(sz10,sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_6682,c_51,c_6577]) ).
cnf(c_6979,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,sK8)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sK8)
| doDivides0(X0,sK8) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_7159,plain,
( sz10 != sz10
| sK8 != sz10
| sz10 = sK8 ),
inference(instantiation,[status(thm)],[c_6649]) ).
cnf(c_7160,plain,
sz10 = sz10,
inference(instantiation,[status(thm)],[c_4616]) ).
cnf(c_7343,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| sz00 = sK8
| sdtlseqdt0(sz10,sK8) ),
inference(superposition,[status(thm)],[c_6266,c_93]) ).
cnf(c_7352,plain,
sdtlseqdt0(sz10,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_7343,c_133,c_134,c_51]) ).
cnf(c_7602,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ sP1(sK8)
| sz00 = sK8
| sz10 = sK8
| sP1(sK5(sK8)) ),
inference(superposition,[status(thm)],[c_116,c_122]) ).
cnf(c_7604,plain,
( ~ aNaturalNumber0(sK5(sK8))
| sP1(sK5(sK8)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7602,c_132,c_133,c_6300]) ).
cnf(c_7948,plain,
( ~ sP1(sK8)
| sz00 = sK8
| sz10 = sK8
| sP1(sK5(sK8)) ),
inference(superposition,[status(thm)],[c_119,c_7604]) ).
cnf(c_7949,plain,
sP1(sK5(sK8)),
inference(forward_subsumption_resolution,[status(thm)],[c_7948,c_132,c_133,c_6300]) ).
cnf(c_8002,plain,
( ~ sP1(sK8)
| sK8 = sz00
| sK8 = sz10
| doDivides0(sK5(sK8),sK8) ),
inference(instantiation,[status(thm)],[c_116]) ).
cnf(c_8003,plain,
( sK5(sK8) != sK8
| ~ sP1(sK8)
| sK8 = sz00
| sK8 = sz10 ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_8007,plain,
( ~ sP1(sK8)
| sK8 = sz00
| sK8 = sz10
| aNaturalNumber0(sK5(sK8)) ),
inference(instantiation,[status(thm)],[c_119]) ).
cnf(c_8009,plain,
( sK5(sK8) != sz10
| ~ sP1(sK8)
| sK8 = sz00
| sK8 = sz10 ),
inference(instantiation,[status(thm)],[c_115]) ).
cnf(c_8665,plain,
( ~ sdtlseqdt0(sK8,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| sz10 = sK8 ),
inference(superposition,[status(thm)],[c_7352,c_80]) ).
cnf(c_8674,plain,
~ sdtlseqdt0(sK8,sz10),
inference(forward_subsumption_resolution,[status(thm)],[c_8665,c_132,c_134,c_51]) ).
cnf(c_9768,plain,
( sdtasdt0(sK5(sK8),sK6(sK8)) = sK8
| sz00 = sK8
| sz10 = sK8 ),
inference(superposition,[status(thm)],[c_6300,c_117]) ).
cnf(c_9769,plain,
( sdtasdt0(sK5(sK5(sK8)),sK6(sK5(sK8))) = sK5(sK8)
| sK5(sK8) = sz00
| sK5(sK8) = sz10 ),
inference(superposition,[status(thm)],[c_7949,c_117]) ).
cnf(c_9771,plain,
sdtasdt0(sK5(sK8),sK6(sK8)) = sK8,
inference(forward_subsumption_resolution,[status(thm)],[c_9768,c_132,c_133]) ).
cnf(c_9802,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sK8),X0)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK8)
| sdtlseqdt0(sK8,X0) ),
inference(superposition,[status(thm)],[c_6578,c_81]) ).
cnf(c_9834,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sK8),X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sK8,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9802,c_134,c_6577]) ).
cnf(c_9942,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| doDivides0(sdtpldt0(sz10,sK8),X0) ),
inference(superposition,[status(thm)],[c_6667,c_101]) ).
cnf(c_9964,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| doDivides0(sdtpldt0(sz10,sK8),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9942,c_49,c_6577]) ).
cnf(c_10010,plain,
( ~ doDivides0(X0,sK5(sK8))
| ~ doDivides0(sK5(sK8),sK8)
| ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK8)
| doDivides0(X0,sK8) ),
inference(instantiation,[status(thm)],[c_6979]) ).
cnf(c_10011,plain,
( ~ doDivides0(sK5(sK8),sK8)
| ~ doDivides0(sz00,sK5(sK8))
| ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK8)
| doDivides0(sz00,sK8) ),
inference(instantiation,[status(thm)],[c_10010]) ).
cnf(c_10110,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sK6(sK8))
| doDivides0(sK5(sK8),sK8) ),
inference(superposition,[status(thm)],[c_9771,c_198]) ).
cnf(c_12755,plain,
( ~ doDivides0(X0,sdtpldt0(sz10,sK8))
| ~ doDivides0(X0,sK8)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK8)
| doDivides0(X0,sz10) ),
inference(superposition,[status(thm)],[c_6562,c_103]) ).
cnf(c_12814,plain,
( ~ doDivides0(X0,sdtpldt0(sz10,sK8))
| ~ doDivides0(X0,sK8)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12755,c_134,c_51]) ).
cnf(c_20248,plain,
( ~ doDivides0(sdtpldt0(sz10,sK8),sK8)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| doDivides0(sdtpldt0(sz10,sK8),sz10) ),
inference(superposition,[status(thm)],[c_6684,c_12814]) ).
cnf(c_20251,plain,
( ~ doDivides0(sdtpldt0(sz10,sK8),sK8)
| doDivides0(sdtpldt0(sz10,sK8),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20248,c_6577]) ).
cnf(c_27425,plain,
( sK5(sK8) != X0
| X1 != X2
| ~ doDivides0(X2,X0)
| doDivides0(X1,sK5(sK8)) ),
inference(instantiation,[status(thm)],[c_4625]) ).
cnf(c_27426,plain,
( sK5(sK8) != sz00
| sz00 != sz00
| ~ doDivides0(sz00,sz00)
| doDivides0(sz00,sK5(sK8)) ),
inference(instantiation,[status(thm)],[c_27425]) ).
cnf(c_36028,plain,
doDivides0(sK5(sK8),sK8),
inference(global_subsumption_just,[status(thm)],[c_10110,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8002]) ).
cnf(c_36035,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sK8)
| sz00 = sK8
| sdtlseqdt0(sK5(sK8),sK8) ),
inference(superposition,[status(thm)],[c_36028,c_104]) ).
cnf(c_36038,plain,
( ~ aNaturalNumber0(sK5(sK8))
| sdtlseqdt0(sK5(sK8),sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36035,c_133,c_134]) ).
cnf(c_36137,plain,
sdtlseqdt0(sK5(sK8),sK8),
inference(global_subsumption_just,[status(thm)],[c_36038,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8007,c_36038]) ).
cnf(c_36143,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sK8)
| sK5(sK8) = sK8
| iLess0(sK5(sK8),sK8) ),
inference(superposition,[status(thm)],[c_36137,c_94]) ).
cnf(c_36144,plain,
( ~ aNaturalNumber0(sK5(sK8))
| sK5(sK8) = sK8
| iLess0(sK5(sK8),sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36143,c_134]) ).
cnf(c_36299,plain,
iLess0(sK5(sK8),sK8),
inference(global_subsumption_just,[status(thm)],[c_36144,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8007,c_8003,c_36144]) ).
cnf(c_36303,plain,
( ~ aNaturalNumber0(sK5(sK8))
| sK5(sK8) = sz00
| sK5(sK8) = sz10
| aNaturalNumber0(sK9(sK5(sK8))) ),
inference(superposition,[status(thm)],[c_36299,c_131]) ).
cnf(c_36304,plain,
( ~ aNaturalNumber0(sK5(sK8))
| sK5(sK8) = sz00
| sK5(sK8) = sz10
| isPrime0(sK9(sK5(sK8))) ),
inference(superposition,[status(thm)],[c_36299,c_124]) ).
cnf(c_37286,plain,
( ~ doDivides0(sz00,sK8)
| ~ aNaturalNumber0(sK8)
| doDivides0(sdtpldt0(sz10,sK8),sz10) ),
inference(superposition,[status(thm)],[c_9964,c_20251]) ).
cnf(c_37287,plain,
( ~ doDivides0(sz00,sK8)
| doDivides0(sdtpldt0(sz10,sK8),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37286,c_134]) ).
cnf(c_37299,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sK8))
| ~ doDivides0(sz00,sK8)
| ~ aNaturalNumber0(sz10)
| sz00 = sz10
| sdtlseqdt0(sdtpldt0(sz10,sK8),sz10) ),
inference(superposition,[status(thm)],[c_37287,c_104]) ).
cnf(c_37305,plain,
( ~ doDivides0(sz00,sK8)
| sdtlseqdt0(sdtpldt0(sz10,sK8),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37299,c_50,c_51,c_6577]) ).
cnf(c_37324,plain,
( sK5(sK8) = sz00
| aNaturalNumber0(sK9(sK5(sK8))) ),
inference(global_subsumption_just,[status(thm)],[c_36303,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8009,c_8007,c_36303]) ).
cnf(c_37624,plain,
( sK5(sK8) = sz00
| isPrime0(sK9(sK5(sK8))) ),
inference(global_subsumption_just,[status(thm)],[c_36304,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8009,c_8007,c_36304]) ).
cnf(c_37630,plain,
( ~ sP1(sK9(sK5(sK8)))
| sK5(sK8) = sz00 ),
inference(superposition,[status(thm)],[c_37624,c_113]) ).
cnf(c_37833,plain,
( ~ doDivides0(sz00,sK8)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sK8,sz10) ),
inference(superposition,[status(thm)],[c_37305,c_9834]) ).
cnf(c_37837,plain,
~ doDivides0(sz00,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_37833,c_8674,c_51]) ).
cnf(c_37838,plain,
~ sP1(sK9(sK5(sK8))),
inference(global_subsumption_just,[status(thm)],[c_37630,c_134,c_49,c_133,c_132,c_142,c_164,c_6300,c_6306,c_6652,c_7159,c_7160,c_8007,c_8002,c_10011,c_27426,c_37630,c_37837]) ).
cnf(c_106522,plain,
sdtasdt0(sK5(sK5(sK8)),sK6(sK5(sK8))) = sK5(sK8),
inference(global_subsumption_just,[status(thm)],[c_9769,c_134,c_49,c_133,c_132,c_142,c_164,c_6300,c_6306,c_6652,c_7159,c_7160,c_8009,c_8007,c_8002,c_9769,c_10011,c_27426,c_37837]) ).
cnf(c_106527,plain,
( ~ aNaturalNumber0(sK5(sK5(sK8)))
| ~ aNaturalNumber0(sK6(sK5(sK8)))
| aNaturalNumber0(sK5(sK8)) ),
inference(superposition,[status(thm)],[c_106522,c_53]) ).
cnf(c_106631,plain,
aNaturalNumber0(sK5(sK8)),
inference(global_subsumption_just,[status(thm)],[c_106527,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8007]) ).
cnf(c_106693,plain,
sdtpldt0(sK5(sK8),sK8) = sdtpldt0(sK8,sK5(sK8)),
inference(superposition,[status(thm)],[c_106631,c_6477]) ).
cnf(c_106699,plain,
sdtasdt0(sz10,sK5(sK8)) = sK5(sK8),
inference(superposition,[status(thm)],[c_106631,c_60]) ).
cnf(c_107209,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sz10)
| sK5(sK8) = sz00
| sdtlseqdt0(sz10,sK5(sK8)) ),
inference(superposition,[status(thm)],[c_106699,c_93]) ).
cnf(c_107224,plain,
( sK5(sK8) = sz00
| sdtlseqdt0(sz10,sK5(sK8)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107209,c_51,c_106631]) ).
cnf(c_108592,plain,
sdtlseqdt0(sz10,sK5(sK8)),
inference(global_subsumption_just,[status(thm)],[c_107224,c_134,c_49,c_133,c_132,c_142,c_164,c_6300,c_6306,c_6652,c_7159,c_7160,c_8007,c_8002,c_10011,c_27426,c_37837,c_107224]) ).
cnf(c_108597,plain,
( ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(sz10)
| sdtpldt0(sz10,sK2(sz10,sK5(sK8))) = sK5(sK8) ),
inference(superposition,[status(thm)],[c_108592,c_74]) ).
cnf(c_108603,plain,
sdtpldt0(sz10,sK2(sz10,sK5(sK8))) = sK5(sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_108597,c_51,c_106631]) ).
cnf(c_113360,plain,
( sK5(sK8) != sz00
| ~ aNaturalNumber0(sK2(sz10,sK5(sK8)))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_108603,c_71]) ).
cnf(c_113379,plain,
( sK5(sK8) != sz00
| ~ aNaturalNumber0(sK2(sz10,sK5(sK8))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_113360,c_50,c_51]) ).
cnf(c_119824,plain,
sK5(sK8) != sz00,
inference(global_subsumption_just,[status(thm)],[c_113379,c_134,c_49,c_133,c_132,c_142,c_164,c_6300,c_6306,c_6652,c_7159,c_7160,c_8007,c_8002,c_10011,c_27426,c_37837]) ).
cnf(c_119828,plain,
aNaturalNumber0(sK9(sK5(sK8))),
inference(backward_subsumption_resolution,[status(thm)],[c_37324,c_119824]) ).
cnf(c_122410,plain,
( ~ doDivides0(X0,sdtpldt0(sK8,sK5(sK8)))
| ~ doDivides0(X0,sK5(sK8))
| ~ aNaturalNumber0(sK5(sK8))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK8)
| doDivides0(X0,sK8) ),
inference(superposition,[status(thm)],[c_106693,c_103]) ).
cnf(c_122468,plain,
( ~ doDivides0(X0,sdtpldt0(sK8,sK5(sK8)))
| ~ doDivides0(X0,sK5(sK8))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122410,c_134,c_106631]) ).
cnf(c_123484,plain,
( ~ doDivides0(X0,sK5(sK8))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_122468,c_134,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8007,c_8002,c_10010]) ).
cnf(c_123495,plain,
( ~ aNaturalNumber0(sK9(sK5(sK8)))
| ~ iLess0(sK5(sK8),sK8)
| ~ aNaturalNumber0(sK5(sK8))
| sK5(sK8) = sz00
| sK5(sK8) = sz10
| doDivides0(sK9(sK5(sK8)),sK8) ),
inference(superposition,[status(thm)],[c_129,c_123484]) ).
cnf(c_123524,plain,
( sK5(sK8) = sz10
| doDivides0(sK9(sK5(sK8)),sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_123495,c_119824,c_106631,c_36299,c_119828]) ).
cnf(c_123544,plain,
doDivides0(sK9(sK5(sK8)),sK8),
inference(global_subsumption_just,[status(thm)],[c_123524,c_49,c_133,c_132,c_142,c_164,c_6300,c_6652,c_7159,c_7160,c_8009,c_123524]) ).
cnf(c_123553,plain,
( ~ aNaturalNumber0(sK9(sK5(sK8)))
| sP1(sK9(sK5(sK8))) ),
inference(superposition,[status(thm)],[c_123544,c_122]) ).
cnf(c_123555,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_123553,c_37838,c_119828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n021.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 07:57:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.23/4.24 % SZS status Started for theBenchmark.p
% 25.23/4.24 % SZS status Theorem for theBenchmark.p
% 25.23/4.24
% 25.23/4.24 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 25.23/4.24
% 25.23/4.24 ------ iProver source info
% 25.23/4.24
% 25.23/4.24 git: date: 2023-05-31 18:12:56 +0000
% 25.23/4.24 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 25.23/4.24 git: non_committed_changes: false
% 25.23/4.24 git: last_make_outside_of_git: false
% 25.23/4.24
% 25.23/4.24 ------ Parsing...
% 25.23/4.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 25.23/4.24
% 25.23/4.24 ------ 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
% 25.23/4.24
% 25.23/4.24 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 25.23/4.24
% 25.23/4.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.23/4.24 ------ Proving...
% 25.23/4.24 ------ Problem Properties
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24 clauses 81
% 25.23/4.24 conjectures 13
% 25.23/4.24 EPR 19
% 25.23/4.24 Horn 46
% 25.23/4.24 unary 8
% 25.23/4.24 binary 10
% 25.23/4.24 lits 325
% 25.23/4.24 lits eq 107
% 25.23/4.24 fd_pure 0
% 25.23/4.24 fd_pseudo 0
% 25.23/4.24 fd_cond 23
% 25.23/4.24 fd_pseudo_cond 13
% 25.23/4.24 AC symbols 0
% 25.23/4.24
% 25.23/4.24 ------ Schedule dynamic 5 is on
% 25.23/4.24
% 25.23/4.24 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24 ------
% 25.23/4.24 Current options:
% 25.23/4.24 ------
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24 ------ Proving...
% 25.23/4.24
% 25.23/4.24
% 25.23/4.24 % SZS status Theorem for theBenchmark.p
% 25.23/4.24
% 25.23/4.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.23/4.24
% 25.23/4.25
%------------------------------------------------------------------------------