TSTP Solution File: NUM498+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:49:35 EDT 2024
% Result : Theorem 189.74s 25.81s
% Output : CNFRefutation 189.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 33
% Syntax : Number of formulae : 313 ( 81 unt; 0 def)
% Number of atoms : 1051 ( 375 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1275 ( 537 ~; 586 |; 109 &)
% ( 12 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 325 ( 0 sgn 197 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( sz10 = xk
| sz00 = xk )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( sz10 = xk
| sz00 = xk )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
inference(negated_conjecture,[],[f46]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f54]) ).
fof(f58,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f60,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f59]) ).
fof(f63,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f71,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f72,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f74,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f76,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f80,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f81,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f85,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f84]) ).
fof(f92,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f93,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f96,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f97,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f101,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f100]) ).
fof(f110,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(f111,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f110]) ).
fof(f116,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn)
& ( sz10 = xk
| sz00 = xk ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f117,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn)
& ( sz10 = xk
| sz00 = xk ) ),
inference(flattening,[],[f116]) ).
fof(f118,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,[],[f76]) ).
fof(f119,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,[],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f121,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])],[f119,f120]) ).
fof(f124,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,[],[f97]) ).
fof(f125,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,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f127,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])],[f125,f126]) ).
fof(f128,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f129,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f128]) ).
fof(f130,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,[],[f111]) ).
fof(f131,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,[],[f130]) ).
fof(f132,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,[],[f131]) ).
fof(f133,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(f134,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])],[f132,f133]) ).
fof(f137,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f138,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f139,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f140,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f142,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f144,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f145,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f146,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f148,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f149,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f150,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f151,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f158,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f160,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f162,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f168,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f169,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f171,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f182,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f186,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f187,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f188,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f190,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f195,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f197,plain,
! [X2,X0] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f205,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f206,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f209,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f210,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f215,plain,
xm != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f217,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f218,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f117]) ).
fof(f219,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f117]) ).
fof(f220,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f117]) ).
fof(f221,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f163]) ).
fof(f227,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f186]) ).
fof(f229,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f188]) ).
fof(f230,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f187]) ).
fof(f232,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f195]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f137]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f139]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f138]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_54,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_58,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_60,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_62,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sz00 ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_72,plain,
( sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f221]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_99,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| X0 = sz00 ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f230]) ).
cnf(c_101,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_110,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X0 = X1
| X0 = sz10 ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_112,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f207]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f206]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f205]) ).
cnf(c_120,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f210]) ).
cnf(c_121,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f209]) ).
cnf(c_125,plain,
xp != xm,
inference(cnf_transformation,[],[f215]) ).
cnf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f217]) ).
cnf(c_129,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f220]) ).
cnf(c_130,negated_conjecture,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f219]) ).
cnf(c_131,negated_conjecture,
( sz00 = xk
| sz10 = xk ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_136,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_154,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_175,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).
cnf(c_179,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_182,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_1636,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_175,c_121]) ).
cnf(c_3392,plain,
X0 = X0,
theory(equality) ).
cnf(c_3394,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3395,plain,
( X0 != X1
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X0) ),
theory(equality) ).
cnf(c_3397,plain,
( X0 != X1
| X2 != X3
| sdtasdt0(X0,X2) = sdtasdt0(X1,X3) ),
theory(equality) ).
cnf(c_3401,plain,
( X0 != X1
| X2 != X3
| ~ doDivides0(X1,X3)
| doDivides0(X0,X2) ),
theory(equality) ).
cnf(c_4667,plain,
( X0 != xp
| X1 != sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| doDivides0(X0,X1) ),
inference(instantiation,[status(thm)],[c_3401]) ).
cnf(c_4789,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(superposition,[status(thm)],[c_49,c_61]) ).
cnf(c_4793,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_118,c_61]) ).
cnf(c_4823,plain,
( X0 != X1
| xm != X1
| xm = X0 ),
inference(instantiation,[status(thm)],[c_3394]) ).
cnf(c_4877,plain,
( X0 != X1
| xn != X1
| xn = X0 ),
inference(instantiation,[status(thm)],[c_3394]) ).
cnf(c_4941,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| doDivides0(sz00,sz00) ),
inference(superposition,[status(thm)],[c_4789,c_179]) ).
cnf(c_4943,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4941,c_51,c_49]) ).
cnf(c_5114,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_3392]) ).
cnf(c_5196,plain,
xm = xm,
inference(instantiation,[status(thm)],[c_3392]) ).
cnf(c_5219,plain,
sdtasdt0(sz10,xp) = xp,
inference(superposition,[status(thm)],[c_116,c_60]) ).
cnf(c_5220,plain,
sdtasdt0(sz10,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_60]) ).
cnf(c_5221,plain,
sdtasdt0(sz10,xn) = xn,
inference(superposition,[status(thm)],[c_118,c_60]) ).
cnf(c_5240,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_116,c_63]) ).
cnf(c_5283,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sz00) ),
inference(superposition,[status(thm)],[c_5240,c_179]) ).
cnf(c_5285,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_5283,c_116,c_49]) ).
cnf(c_5444,plain,
( X0 != sdtasdt0(xn,xm)
| xp != xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| doDivides0(xp,X0) ),
inference(instantiation,[status(thm)],[c_4667]) ).
cnf(c_5445,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_3392]) ).
cnf(c_5980,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_3394,c_3392]) ).
cnf(c_6018,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(superposition,[status(thm)],[c_5219,c_93]) ).
cnf(c_6021,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(superposition,[status(thm)],[c_5220,c_93]) ).
cnf(c_6022,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| sz00 = xn
| sdtlseqdt0(sz10,xn) ),
inference(superposition,[status(thm)],[c_5221,c_93]) ).
cnf(c_6031,plain,
( sz00 = xn
| sdtlseqdt0(sz10,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6022,c_118,c_51]) ).
cnf(c_6032,plain,
( sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6021,c_117,c_51]) ).
cnf(c_6033,plain,
( sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6018,c_116,c_51]) ).
cnf(c_6438,plain,
( xp != X0
| xn != X1
| ~ doDivides0(X0,X1)
| doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_3401]) ).
cnf(c_6710,plain,
( sz00 = xk
| xk = sz10 ),
inference(resolution,[status(thm)],[c_5980,c_131]) ).
cnf(c_6791,plain,
( ~ doDivides0(X0,xm)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| doDivides0(xp,xm) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_6792,plain,
( ~ doDivides0(sz00,xm)
| ~ doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| doDivides0(xp,xm) ),
inference(instantiation,[status(thm)],[c_6791]) ).
cnf(c_6793,plain,
( ~ doDivides0(X0,xn)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_6794,plain,
( ~ doDivides0(sz00,xn)
| ~ doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_6793]) ).
cnf(c_7053,plain,
( ~ aNaturalNumber0(sz10)
| sz00 = xk
| aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_6710,c_3395]) ).
cnf(c_7064,plain,
( sz00 = xk
| aNaturalNumber0(xk) ),
inference(global_subsumption_just,[status(thm)],[c_7053,c_51,c_7053]) ).
cnf(c_7086,plain,
( xk = sz00
| aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_7064,c_5980]) ).
cnf(c_7924,plain,
( ~ aNaturalNumber0(sz00)
| aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_7086,c_3395]) ).
cnf(c_8661,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| aNaturalNumber0(sdtpldt0(sz10,X0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_9176,plain,
( X0 != X1
| xm != X2
| ~ doDivides0(X1,X2)
| doDivides0(X0,xm) ),
inference(instantiation,[status(thm)],[c_3401]) ).
cnf(c_9177,plain,
( sz00 != sz00
| xm != sz00
| ~ doDivides0(sz00,sz00)
| doDivides0(sz00,xm) ),
inference(instantiation,[status(thm)],[c_9176]) ).
cnf(c_9184,plain,
( X0 != X1
| xn != X2
| ~ doDivides0(X1,X2)
| doDivides0(X0,xn) ),
inference(instantiation,[status(thm)],[c_3401]) ).
cnf(c_9185,plain,
( sz00 != sz00
| xn != sz00
| ~ doDivides0(sz00,sz00)
| doDivides0(sz00,xn) ),
inference(instantiation,[status(thm)],[c_9184]) ).
cnf(c_9340,plain,
( xp != xp
| xn != X0
| ~ doDivides0(xp,X0)
| doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_6438]) ).
cnf(c_9362,plain,
( sdtasdt0(X0,X1) != X2
| xn != X2
| xn = sdtasdt0(X0,X1) ),
inference(instantiation,[status(thm)],[c_4877]) ).
cnf(c_10046,plain,
( X0 != xm
| xm != xm
| xm = X0 ),
inference(instantiation,[status(thm)],[c_4823]) ).
cnf(c_10047,plain,
( sz00 != xm
| xm != xm
| xm = sz00 ),
inference(instantiation,[status(thm)],[c_10046]) ).
cnf(c_17101,plain,
( X0 != xn
| xn != xn
| xn = X0 ),
inference(instantiation,[status(thm)],[c_4877]) ).
cnf(c_17102,plain,
( sz00 != xn
| xn != xn
| xn = sz00 ),
inference(instantiation,[status(thm)],[c_17101]) ).
cnf(c_17571,plain,
( sdtasdt0(X0,X1) != xn
| xn != xn
| xn = sdtasdt0(X0,X1) ),
inference(instantiation,[status(thm)],[c_9362]) ).
cnf(c_25661,plain,
( ~ aNaturalNumber0(sz10)
| aNaturalNumber0(sdtpldt0(sz10,sz10)) ),
inference(instantiation,[status(thm)],[c_8661]) ).
cnf(c_25936,plain,
( X0 != X1
| xn != xn
| sdtasdt0(xn,X0) = sdtasdt0(xn,X1) ),
inference(instantiation,[status(thm)],[c_3397]) ).
cnf(c_30760,plain,
( xp != xp
| xn != sdtasdt0(xn,sz10)
| ~ doDivides0(xp,sdtasdt0(xn,sz10))
| doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_9340]) ).
cnf(c_40133,plain,
( sdtasdt0(xn,sz10) != sdtasdt0(xn,xm)
| xp != xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| doDivides0(xp,sdtasdt0(xn,sz10)) ),
inference(instantiation,[status(thm)],[c_5444]) ).
cnf(c_44522,plain,
( sdtasdt0(xn,sz10) != xn
| xn != xn
| xn = sdtasdt0(xn,sz10) ),
inference(instantiation,[status(thm)],[c_17571]) ).
cnf(c_111488,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_51,c_56]) ).
cnf(c_111503,plain,
sdtasdt0(sz10,xp) = xp,
inference(superposition,[status(thm)],[c_116,c_60]) ).
cnf(c_111504,plain,
sdtasdt0(sz10,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_60]) ).
cnf(c_111505,plain,
sdtasdt0(sz10,xn) = xn,
inference(superposition,[status(thm)],[c_118,c_60]) ).
cnf(c_111517,plain,
sdtasdt0(sz00,xp) = sz00,
inference(superposition,[status(thm)],[c_116,c_62]) ).
cnf(c_111606,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[c_111488,c_182]) ).
cnf(c_111613,plain,
sdtlseqdt0(sz00,sz10),
inference(forward_subsumption_resolution,[status(thm)],[c_111606,c_51,c_49]) ).
cnf(c_111641,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_49,c_58]) ).
cnf(c_111642,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_51,c_58]) ).
cnf(c_111645,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
cnf(c_111646,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
cnf(c_111773,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(superposition,[status(thm)],[c_111503,c_93]) ).
cnf(c_111776,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(superposition,[status(thm)],[c_111504,c_93]) ).
cnf(c_111777,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| sz00 = xn
| sdtlseqdt0(sz10,xn) ),
inference(superposition,[status(thm)],[c_111505,c_93]) ).
cnf(c_111783,plain,
( sz00 = xn
| sdtlseqdt0(sz10,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111777,c_118,c_51]) ).
cnf(c_111784,plain,
( sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111776,c_117,c_51]) ).
cnf(c_111785,plain,
( sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111773,c_116,c_51]) ).
cnf(c_111790,plain,
sdtlseqdt0(sz10,xn),
inference(global_subsumption_just,[status(thm)],[c_111783,c_118,c_116,c_49,c_130,c_136,c_154,c_4943,c_5114,c_5285,c_6031,c_6794,c_9185,c_17102]) ).
cnf(c_111792,plain,
sdtlseqdt0(sz10,xm),
inference(global_subsumption_just,[status(thm)],[c_111784,c_117,c_116,c_49,c_129,c_136,c_154,c_4943,c_5196,c_5285,c_6032,c_6792,c_9177,c_10047]) ).
cnf(c_111794,plain,
sdtlseqdt0(sz10,xp),
inference(global_subsumption_just,[status(thm)],[c_111785,c_1636,c_6033]) ).
cnf(c_111806,plain,
sdtasdt0(sz00,xp) = sdtasdt0(xp,sz00),
inference(superposition,[status(thm)],[c_116,c_111641]) ).
cnf(c_112009,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| sdtpldt0(sz10,sK0(sz10,xn)) = xn ),
inference(superposition,[status(thm)],[c_111790,c_74]) ).
cnf(c_112010,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sdtpldt0(sz10,sK0(sz10,xm)) = xm ),
inference(superposition,[status(thm)],[c_111792,c_74]) ).
cnf(c_112011,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sz10,sK0(sz10,xp)) = xp ),
inference(superposition,[status(thm)],[c_111794,c_74]) ).
cnf(c_112019,plain,
sdtpldt0(sz10,sK0(sz10,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_112011,c_116,c_51]) ).
cnf(c_112020,plain,
sdtpldt0(sz10,sK0(sz10,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_112010,c_117,c_51]) ).
cnf(c_112021,plain,
sdtpldt0(sz10,sK0(sz10,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_112009,c_118,c_51]) ).
cnf(c_112164,plain,
( ~ sdtlseqdt0(sz10,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_111613,c_80]) ).
cnf(c_112187,plain,
~ sdtlseqdt0(sz10,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_112164,c_50,c_51,c_49]) ).
cnf(c_112234,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sz00 = xp
| aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_128,c_100]) ).
cnf(c_112248,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112234,c_116,c_120]) ).
cnf(c_112729,plain,
sdtasdt0(sz10,xp) = sdtasdt0(xp,sz10),
inference(superposition,[status(thm)],[c_116,c_111642]) ).
cnf(c_112827,plain,
( sz00 != xp
| ~ aNaturalNumber0(sK0(sz10,xp))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_112019,c_71]) ).
cnf(c_112833,plain,
( sz00 != xp
| ~ aNaturalNumber0(sK0(sz10,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112827,c_50,c_51]) ).
cnf(c_112840,plain,
( sz00 != xm
| ~ aNaturalNumber0(sK0(sz10,xm))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_112020,c_71]) ).
cnf(c_112846,plain,
( sz00 != xm
| ~ aNaturalNumber0(sK0(sz10,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112840,c_50,c_51]) ).
cnf(c_113018,plain,
sz00 != xp,
inference(global_subsumption_just,[status(thm)],[c_112833,c_1636]) ).
cnf(c_113025,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| aNaturalNumber0(xk) ),
inference(backward_subsumption_resolution,[status(thm)],[c_112248,c_113018]) ).
cnf(c_113055,plain,
aNaturalNumber0(xk),
inference(global_subsumption_just,[status(thm)],[c_113025,c_49,c_7924]) ).
cnf(c_113064,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xk) = sdtpldt0(xk,X0) ),
inference(superposition,[status(thm)],[c_113055,c_54]) ).
cnf(c_113066,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(superposition,[status(thm)],[c_113055,c_111645]) ).
cnf(c_113446,plain,
sz00 != xm,
inference(global_subsumption_just,[status(thm)],[c_112846,c_117,c_116,c_49,c_129,c_136,c_154,c_4943,c_5196,c_5285,c_6792,c_9177,c_10047]) ).
cnf(c_113467,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_118,c_111646]) ).
cnf(c_114015,plain,
( sz00 != xn
| ~ aNaturalNumber0(sK0(sz10,xn))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_112021,c_71]) ).
cnf(c_114027,plain,
( sz00 != xn
| ~ aNaturalNumber0(sK0(sz10,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114015,c_50,c_51]) ).
cnf(c_114312,plain,
sz00 != xn,
inference(global_subsumption_just,[status(thm)],[c_114027,c_118,c_116,c_49,c_130,c_136,c_154,c_4943,c_5114,c_5285,c_6794,c_9185,c_17102]) ).
cnf(c_114375,plain,
sdtpldt0(sz10,xk) = sdtpldt0(xk,sz10),
inference(superposition,[status(thm)],[c_51,c_113064]) ).
cnf(c_115608,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_113066,c_53]) ).
cnf(c_115609,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sz00 = xp
| sdtlseqdt0(xk,sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_113066,c_93]) ).
cnf(c_115616,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_115608,c_113055,c_116]) ).
cnf(c_115618,plain,
sdtlseqdt0(xk,sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_115609,c_113018,c_113055,c_116]) ).
cnf(c_115655,plain,
sdtasdt0(sz10,sdtasdt0(xp,xk)) = sdtasdt0(xp,xk),
inference(superposition,[status(thm)],[c_115616,c_60]) ).
cnf(c_115684,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,X0) ),
inference(superposition,[status(thm)],[c_115618,c_81]) ).
cnf(c_115693,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xk,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_115684,c_113055,c_115616]) ).
cnf(c_116075,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm)],[c_128,c_113467]) ).
cnf(c_116076,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm)],[c_120,c_113467]) ).
cnf(c_116079,plain,
( sdtasdt0(xm,xn) != sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xm
| sz00 = xn ),
inference(superposition,[status(thm)],[c_113467,c_72]) ).
cnf(c_116081,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_113467,c_53]) ).
cnf(c_116089,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_116081,c_118,c_117]) ).
cnf(c_116092,plain,
sdtasdt0(xm,xn) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_116079,c_114312,c_113446,c_118,c_117]) ).
cnf(c_116129,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(sdtasdt0(xm,xn),xp)) = sdtasdt0(xm,xn)
| sz00 = xp ),
inference(superposition,[status(thm)],[c_116076,c_99]) ).
cnf(c_116138,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xm,xn),xp)) = sdtasdt0(xm,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_116129,c_113018,c_116,c_116089]) ).
cnf(c_117173,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_114375,c_52]) ).
cnf(c_117183,plain,
aNaturalNumber0(sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_117173,c_113055,c_51]) ).
cnf(c_117198,plain,
( sz00 = xk
| aNaturalNumber0(sdtpldt0(sz10,sz10)) ),
inference(superposition,[status(thm)],[c_131,c_117183]) ).
cnf(c_117252,plain,
aNaturalNumber0(sdtpldt0(sz10,sz10)),
inference(global_subsumption_just,[status(thm)],[c_117198,c_51,c_25661]) ).
cnf(c_117281,plain,
sdtasdt0(sz10,sdtpldt0(sz10,sz10)) = sdtpldt0(sz10,sz10),
inference(superposition,[status(thm)],[c_117252,c_60]) ).
cnf(c_118153,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(sz10,sdtpldt0(sz10,sz10)) ),
inference(superposition,[status(thm)],[c_117281,c_93]) ).
cnf(c_118162,plain,
( sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(sz10,sdtpldt0(sz10,sz10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_118153,c_51,c_117252]) ).
cnf(c_118215,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sz10),X0)
| ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_118162,c_81]) ).
cnf(c_118224,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sz10),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_118215,c_51,c_117252]) ).
cnf(c_124083,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtpldt0(sz10,sz10))
| sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_82,c_118224]) ).
cnf(c_124117,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtpldt0(sz10,sz10))
| sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124083,c_117252]) ).
cnf(c_124127,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sz10),X0)
| ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(sz10,X1) ),
inference(superposition,[status(thm)],[c_124117,c_81]) ).
cnf(c_124165,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sz10),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(sz10,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124127,c_117252]) ).
cnf(c_125948,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xp,xk) = sz00
| sdtlseqdt0(sz10,sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_115655,c_93]) ).
cnf(c_125957,plain,
( sdtasdt0(xp,xk) = sz00
| sdtlseqdt0(sz10,sdtasdt0(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_125948,c_51,c_115616]) ).
cnf(c_149230,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtpldt0(sz10,sz10))
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(sz10,X1) ),
inference(superposition,[status(thm)],[c_82,c_124165]) ).
cnf(c_149331,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtpldt0(sz10,sz10))
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(sz10,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149230,c_117252]) ).
cnf(c_157319,plain,
( sz10 != xm
| xn != xn
| sdtasdt0(xn,sz10) = sdtasdt0(xn,xm) ),
inference(instantiation,[status(thm)],[c_25936]) ).
cnf(c_223773,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xk,sdtpldt0(sz10,sz10))
| sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_149331,c_115693]) ).
cnf(c_223884,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xk,sdtpldt0(sz10,sz10))
| sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_223773,c_115616,c_117252]) ).
cnf(c_227096,plain,
sdtasdt0(xp,xk) = sdtasdt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_116138,c_116075]) ).
cnf(c_227113,plain,
sdtasdt0(xp,xk) != sz00,
inference(demodulation,[status(thm)],[c_116092,c_227096]) ).
cnf(c_227133,plain,
sdtlseqdt0(sz10,sdtasdt0(xp,xk)),
inference(backward_subsumption_resolution,[status(thm)],[c_125957,c_227113]) ).
cnf(c_227158,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| doDivides0(xm,sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_227096,c_179]) ).
cnf(c_227174,plain,
doDivides0(xm,sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_227158,c_118,c_117]) ).
cnf(c_227662,plain,
( sz00 = xk
| doDivides0(xm,sdtasdt0(xp,sz10)) ),
inference(superposition,[status(thm)],[c_131,c_227174]) ).
cnf(c_227848,plain,
( sz00 = xk
| doDivides0(xm,xp) ),
inference(light_normalisation,[status(thm)],[c_227662,c_111503,c_112729]) ).
cnf(c_227854,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ isPrime0(xp)
| sz00 = xk
| sz10 = xm
| xp = xm ),
inference(superposition,[status(thm)],[c_227848,c_110]) ).
cnf(c_227862,plain,
( sz00 = xk
| sz10 = xm ),
inference(forward_subsumption_resolution,[status(thm)],[c_227854,c_125,c_121,c_117,c_116]) ).
cnf(c_227878,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz10,sz10) = sz00
| sz00 = xk
| sdtlseqdt0(X0,sdtasdt0(xp,sz10))
| sdtlseqdt0(xk,sdtpldt0(sz10,sz10))
| sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_131,c_223884]) ).
cnf(c_227979,plain,
sz00 = xk,
inference(global_subsumption_just,[status(thm)],[c_227878,c_130,c_120,c_4793,c_5114,c_5445,c_30760,c_40133,c_44522,c_157319,c_227862]) ).
cnf(c_227983,plain,
sdtlseqdt0(sz10,sdtasdt0(xp,sz00)),
inference(demodulation,[status(thm)],[c_227133,c_227979]) ).
cnf(c_228401,plain,
sdtlseqdt0(sz10,sz00),
inference(light_normalisation,[status(thm)],[c_227983,c_111517,c_111806]) ).
cnf(c_228402,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_228401,c_112187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 20:02:58 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 189.74/25.81 % SZS status Started for theBenchmark.p
% 189.74/25.81 % SZS status Theorem for theBenchmark.p
% 189.74/25.81
% 189.74/25.81 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 189.74/25.81
% 189.74/25.81 ------ iProver source info
% 189.74/25.81
% 189.74/25.81 git: date: 2024-05-02 19:28:25 +0000
% 189.74/25.81 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 189.74/25.81 git: non_committed_changes: false
% 189.74/25.81
% 189.74/25.81 ------ Parsing...
% 189.74/25.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 189.74/25.81
% 189.74/25.81 ------ 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
% 189.74/25.81
% 189.74/25.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 189.74/25.81
% 189.74/25.81 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 189.74/25.81 ------ Proving...
% 189.74/25.81 ------ Problem Properties
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81 clauses 78
% 189.74/25.81 conjectures 3
% 189.74/25.81 EPR 27
% 189.74/25.81 Horn 52
% 189.74/25.81 unary 19
% 189.74/25.81 binary 8
% 189.74/25.81 lits 274
% 189.74/25.81 lits eq 76
% 189.74/25.81 fd_pure 0
% 189.74/25.81 fd_pseudo 0
% 189.74/25.81 fd_cond 15
% 189.74/25.81 fd_pseudo_cond 11
% 189.74/25.81 AC symbols 0
% 189.74/25.81
% 189.74/25.81 ------ Input Options Time Limit: Unbounded
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81 ------
% 189.74/25.81 Current options:
% 189.74/25.81 ------
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81 ------ Proving...
% 189.74/25.81
% 189.74/25.81
% 189.74/25.81 % SZS status Theorem for theBenchmark.p
% 189.74/25.81
% 189.74/25.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 189.74/25.82
% 189.74/25.83
%------------------------------------------------------------------------------