TSTP Solution File: NUM503+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 11:30:58 EDT 2023
% Result : Theorem 20.17s 3.67s
% Output : CNFRefutation 20.17s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f246)
% 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
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(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
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(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& sz00 != X0 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sz00 != X1
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/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(f43,axiom,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
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(f47,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f50,axiom,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2389) ).
fof(f51,conjecture,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(negated_conjecture,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f69,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f77,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f79,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f81,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f83,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f90,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f97,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f98,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f102,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f103,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(f104,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,[],[f103]) ).
fof(f111,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f112,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f115,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(f116,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f122,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(ennf_transformation,[],[f52]) ).
fof(f123,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,[],[f81]) ).
fof(f124,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,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f126,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])],[f124,f125]) ).
fof(f127,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f128,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f127]) ).
fof(f129,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,[],[f102]) ).
fof(f130,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,[],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,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])],[f130,f131]) ).
fof(f133,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,[],[f104]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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,[],[f116]) ).
fof(f136,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,[],[f135]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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(f139,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])],[f137,f138]) ).
fof(f142,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f143,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f144,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f145,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f146,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f149,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f150,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f153,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f155,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f161,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f162,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f165,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f167,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f171,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f176,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f182,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f187,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f191,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f192,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f198,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f200,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f212,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f215,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f217,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f43]) ).
fof(f218,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f219,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f222,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f225,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f232,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f50]) ).
fof(f233,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f122]) ).
fof(f234,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f235,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f240,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f191]) ).
fof(f242,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f243,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f192]) ).
fof(f245,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f200]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f142]) ).
cnf(c_50,negated_conjecture,
sz00 != sz10,
inference(cnf_transformation,[],[f144]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f143]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_68,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00 ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_69,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_72,plain,
( sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f234]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_76,plain,
( ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X0,X1),X0) = X1 ),
inference(cnf_transformation,[],[f235]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_83,plain,
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f246]) ).
cnf(c_88,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_90,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1)) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f187]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_99,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| X0 = sz00 ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_104,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_112,negated_conjecture,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f245]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f212]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f211]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f210]) ).
cnf(c_120,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f215]) ).
cnf(c_121,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f214]) ).
cnf(c_123,negated_conjecture,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f217]) ).
cnf(c_126,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f219]) ).
cnf(c_127,negated_conjecture,
xp != xn,
inference(cnf_transformation,[],[f218]) ).
cnf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f222]) ).
cnf(c_132,negated_conjecture,
sz00 != xk,
inference(cnf_transformation,[],[f225]) ).
cnf(c_138,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f232]) ).
cnf(c_139,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_140,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(sz00,sz00) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_144,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_162,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_187,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_190,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_193,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X0,X1),X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_76,c_52,c_76,c_190]) ).
cnf(c_239,plain,
X0 = X0,
theory(equality) ).
cnf(c_241,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_242,plain,
( X0 != X1
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X0) ),
theory(equality) ).
cnf(c_245,plain,
( X0 != X1
| X2 != X3
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X0,X2) ),
theory(equality) ).
cnf(c_252,plain,
( X0 != X1
| ~ isPrime0(X1)
| isPrime0(X0) ),
theory(equality) ).
cnf(c_265,plain,
( X0 != xp
| ~ isPrime0(xp)
| isPrime0(X0) ),
inference(instantiation,[status(thm)],[c_252]) ).
cnf(c_266,plain,
( sz00 != xp
| ~ isPrime0(xp)
| isPrime0(sz00) ),
inference(instantiation,[status(thm)],[c_265]) ).
cnf(c_308,plain,
( xp != X0
| xm != X1
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_245]) ).
cnf(c_310,plain,
( sdtasdt0(xp,xm) != X0
| sdtasdt0(xn,xm) != X1
| ~ sdtlseqdt0(X1,X0)
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_245]) ).
cnf(c_321,plain,
( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_336,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_51,c_56]) ).
cnf(c_338,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_56]) ).
cnf(c_446,plain,
( X0 != X1
| xp != X1
| X0 = xp ),
inference(instantiation,[status(thm)],[c_241]) ).
cnf(c_447,plain,
( sz00 != sz00
| xp != sz00
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_446]) ).
cnf(c_456,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_116,c_63]) ).
cnf(c_582,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[c_336,c_190]) ).
cnf(c_584,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz00,xm) ),
inference(superposition,[status(thm)],[c_338,c_190]) ).
cnf(c_610,plain,
( X0 != X1
| xm != X1
| xm = X0 ),
inference(instantiation,[status(thm)],[c_241]) ).
cnf(c_686,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_82,c_139]) ).
cnf(c_909,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xm)
| sdtlseqdt0(xm,X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_917,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1383,plain,
xm = xm,
inference(instantiation,[status(thm)],[c_239]) ).
cnf(c_1466,plain,
( sdtasdt0(xp,xm) != X0
| sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_310]) ).
cnf(c_1467,plain,
sdtasdt0(xn,xm) = sdtasdt0(xn,xm),
inference(instantiation,[status(thm)],[c_239]) ).
cnf(c_1639,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xp,X0)) ),
inference(instantiation,[status(thm)],[c_187]) ).
cnf(c_1770,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_239]) ).
cnf(c_2203,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_2626,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_56]) ).
cnf(c_2725,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz00,xm) ),
inference(superposition,[status(thm)],[c_2626,c_190]) ).
cnf(c_2827,plain,
sdtlseqdt0(sz00,xm),
inference(global_subsumption_just,[status(thm)],[c_2725,c_117,c_49,c_584]) ).
cnf(c_3538,plain,
( ~ sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| sz00 = xm ),
inference(superposition,[status(thm)],[c_2827,c_80]) ).
cnf(c_3551,plain,
( sdtasdt0(xp,xm) != sdtasdt0(xn,xm)
| sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_1466]) ).
cnf(c_3552,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_3844,plain,
( xp != xp
| xm != X0
| ~ sdtlseqdt0(xp,X0)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_308]) ).
cnf(c_3847,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_3884,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_321]) ).
cnf(c_5771,plain,
sdtasdt0(xp,sz10) = xp,
inference(superposition,[status(thm)],[c_116,c_61]) ).
cnf(c_5864,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_82,c_139]) ).
cnf(c_5899,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_5864,c_118,c_117,c_116,c_686,c_917,c_2203]) ).
cnf(c_6714,plain,
( X0 != X1
| xm != X2
| ~ sdtlseqdt0(X2,X1)
| sdtlseqdt0(xm,X0) ),
inference(instantiation,[status(thm)],[c_245]) ).
cnf(c_6715,plain,
( sz00 != sz00
| xm != sz00
| ~ sdtlseqdt0(sz00,sz00)
| sdtlseqdt0(xm,sz00) ),
inference(instantiation,[status(thm)],[c_6714]) ).
cnf(c_6811,plain,
( X0 != xm
| xm != xm
| xm = X0 ),
inference(instantiation,[status(thm)],[c_610]) ).
cnf(c_6812,plain,
( sz00 != xm
| xm != xm
| xm = sz00 ),
inference(instantiation,[status(thm)],[c_6811]) ).
cnf(c_7251,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xm,xk)
| sdtlseqdt0(xk,xm) ),
inference(instantiation,[status(thm)],[c_909]) ).
cnf(c_8010,plain,
( sdtasdt0(xp,X0) != X1
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(xp,X0)) ),
inference(instantiation,[status(thm)],[c_242]) ).
cnf(c_8011,plain,
( sdtasdt0(xp,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| aNaturalNumber0(sdtasdt0(xp,sz00)) ),
inference(instantiation,[status(thm)],[c_8010]) ).
cnf(c_9549,plain,
( xp != xp
| xm != xk
| ~ sdtlseqdt0(xp,xk)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_3844]) ).
cnf(c_10621,plain,
( sdtasdt0(xp,X0) != xp
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| X0 = sz10
| sz00 = xp ),
inference(superposition,[status(thm)],[c_5771,c_69]) ).
cnf(c_10650,plain,
( sdtasdt0(xp,sz00) != xp
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sz00 = sz10
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_10621]) ).
cnf(c_10951,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xm
| xp = xn ),
inference(superposition,[status(thm)],[c_88,c_139]) ).
cnf(c_11376,plain,
( sz00 = xm
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_10951,c_118,c_117,c_116,c_126,c_127,c_10951]) ).
cnf(c_11377,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xm ),
inference(renaming,[status(thm)],[c_11376]) ).
cnf(c_11609,plain,
( ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| X0 = sz10
| sz00 = xp
| sdtlseqdt0(sdtasdt0(xp,X0),xp) ),
inference(superposition,[status(thm)],[c_5771,c_90]) ).
cnf(c_11638,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xp
| sz00 = xm
| xm = xk ),
inference(superposition,[status(thm)],[c_90,c_11377]) ).
cnf(c_11639,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xp
| xm = xk
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_90,c_5899]) ).
cnf(c_11654,plain,
( ~ sdtlseqdt0(sz00,sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sz00 = sz10
| sz00 = xp
| sdtlseqdt0(sdtasdt0(xp,sz00),xp) ),
inference(instantiation,[status(thm)],[c_11609]) ).
cnf(c_12447,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_116,c_63]) ).
cnf(c_12449,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_63]) ).
cnf(c_12524,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_82,c_139]) ).
cnf(c_12559,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_12524,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_266,c_917,c_1770,c_3847,c_3884,c_7251,c_9549,c_11639]) ).
cnf(c_12806,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtpldt0(sdtasdt0(xp,xm),sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_12559,c_74]) ).
cnf(c_12875,plain,
( sdtpldt0(sdtasdt0(xp,xm),sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_12806,c_118,c_117,c_116,c_917,c_2203,c_12806]) ).
cnf(c_12880,plain,
( ~ aNaturalNumber0(sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_12875,c_52]) ).
cnf(c_12887,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_12880,c_118,c_117,c_917]) ).
cnf(c_12889,plain,
( ~ aNaturalNumber0(X0)
| sdtmndt0(sdtpldt0(X0,sdtasdt0(xn,xm)),X0) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_12887,c_193]) ).
cnf(c_12920,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_12559,c_80]) ).
cnf(c_13017,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_12920,c_118,c_117,c_116,c_917,c_2203,c_12920]) ).
cnf(c_13223,plain,
sdtmndt0(sdtpldt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)),sdtasdt0(xn,xm)) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_12887,c_12889]) ).
cnf(c_14310,plain,
( ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xm
| xp = xn ),
inference(superposition,[status(thm)],[c_88,c_13017]) ).
cnf(c_14563,plain,
( sz00 = xm
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(global_subsumption_just,[status(thm)],[c_14310,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_266,c_917,c_1770,c_3847,c_3884,c_7251,c_9549,c_11638]) ).
cnf(c_14564,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| sz00 = xm ),
inference(renaming,[status(thm)],[c_14563]) ).
cnf(c_14590,plain,
( sdtmndt0(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sz00 = xm ),
inference(superposition,[status(thm)],[c_14564,c_13223]) ).
cnf(c_16174,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| xp = xn
| xm = sz00 ),
inference(resolution,[status(thm)],[c_68,c_139]) ).
cnf(c_16785,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| xm = sz00 ),
inference(global_subsumption_just,[status(thm)],[c_16174,c_118,c_117,c_116,c_127,c_917,c_1383,c_1467,c_3551,c_3552,c_6812,c_11377,c_16174]) ).
cnf(c_16786,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| xm = sz00 ),
inference(renaming,[status(thm)],[c_16785]) ).
cnf(c_16812,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| xp = sz00
| xm = sz00
| xm = xk ),
inference(resolution,[status(thm)],[c_16786,c_69]) ).
cnf(c_16814,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ isPrime0(sdtasdt0(xp,xk))
| xm = sz00
| isPrime0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c_16786,c_252]) ).
cnf(c_16824,plain,
( xm = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_16814,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_144,c_162,c_266,c_447,c_917,c_1770,c_3847,c_9549,c_16812]) ).
cnf(c_16825,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| xm = sz00 ),
inference(renaming,[status(thm)],[c_16824]) ).
cnf(c_16836,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| xp = sz00
| xm = sz00
| xm = xk ),
inference(resolution,[status(thm)],[c_16825,c_90]) ).
cnf(c_17153,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_1639]) ).
cnf(c_18895,plain,
sz00 = xm,
inference(global_subsumption_just,[status(thm)],[c_14590,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_140,c_144,c_162,c_266,c_447,c_917,c_1770,c_3538,c_3847,c_3884,c_6715,c_7251,c_9549,c_16836]) ).
cnf(c_18954,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,sz00),sdtasdt0(xp,sz00))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_18895,c_13017]) ).
cnf(c_20091,plain,
( ~ sdtlseqdt0(sz00,sdtasdt0(xp,sz00))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_12449,c_18954]) ).
cnf(c_21020,plain,
( ~ sdtlseqdt0(sz00,sz00)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_12447,c_20091]) ).
cnf(c_25495,negated_conjecture,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_139,c_49,c_140,c_21020]) ).
cnf(c_25497,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_25495,c_120]) ).
cnf(c_25499,plain,
( sdtsldt0(sdtasdt0(xp,xm),xp) = xk
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_25495,c_128]) ).
cnf(c_25500,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(global_subsumption_just,[status(thm)],[c_25497,c_117,c_116,c_17153]) ).
cnf(c_25769,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sz00 = xm
| sdtlseqdt0(xn,sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_25495,c_93]) ).
cnf(c_25828,plain,
sz00 = xm,
inference(global_subsumption_just,[status(thm)],[c_25769,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_140,c_144,c_162,c_266,c_447,c_917,c_1770,c_3538,c_3847,c_3884,c_6715,c_7251,c_9549,c_16836]) ).
cnf(c_25955,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_25500,c_104]) ).
cnf(c_26447,plain,
( sdtasdt0(xp,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_25955,c_117,c_116,c_2203,c_25955]) ).
cnf(c_26449,plain,
( sdtasdt0(xp,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xp,sz00)) ),
inference(superposition,[status(thm)],[c_25828,c_26447]) ).
cnf(c_26457,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,sz00),xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sz00))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sz00) = xp
| sdtasdt0(xp,xm) = sz00 ),
inference(superposition,[status(thm)],[c_26449,c_80]) ).
cnf(c_26646,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(sdtasdt0(xp,xm),xp)) = sdtasdt0(xp,xm)
| sz00 = xp ),
inference(superposition,[status(thm)],[c_25500,c_99]) ).
cnf(c_27004,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xp,xm),xp)) = sdtasdt0(xp,xm),
inference(global_subsumption_just,[status(thm)],[c_26646,c_121,c_117,c_116,c_49,c_112,c_266,c_2203,c_26646]) ).
cnf(c_27006,plain,
sdtasdt0(xp,xm) = sdtasdt0(xp,xk),
inference(superposition,[status(thm)],[c_25499,c_27004]) ).
cnf(c_27013,plain,
( sdtasdt0(xp,xm) != sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sz00 = xp
| sz00 = xk ),
inference(superposition,[status(thm)],[c_27006,c_72]) ).
cnf(c_27017,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27013,c_26457,c_11654,c_10650,c_8011,c_3847,c_917,c_582,c_456,c_266,c_112,c_120,c_50,c_132,c_49,c_51,c_116,c_117,c_118,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 09:56:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.17/3.67 % SZS status Started for theBenchmark.p
% 20.17/3.67 % SZS status Theorem for theBenchmark.p
% 20.17/3.67
% 20.17/3.67 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 20.17/3.67
% 20.17/3.67 ------ iProver source info
% 20.17/3.67
% 20.17/3.67 git: date: 2023-05-31 18:12:56 +0000
% 20.17/3.67 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 20.17/3.67 git: non_committed_changes: false
% 20.17/3.67 git: last_make_outside_of_git: false
% 20.17/3.67
% 20.17/3.67 ------ Parsing...
% 20.17/3.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.17/3.67
% 20.17/3.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 20.17/3.67
% 20.17/3.67 ------ Preprocessing...
% 20.17/3.67
% 20.17/3.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.17/3.67 ------ Proving...
% 20.17/3.67 ------ Problem Properties
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67 clauses 84
% 20.17/3.67 conjectures 10
% 20.17/3.67 EPR 31
% 20.17/3.67 Horn 58
% 20.17/3.67 unary 25
% 20.17/3.67 binary 7
% 20.17/3.67 lits 282
% 20.17/3.67 lits eq 78
% 20.17/3.67 fd_pure 0
% 20.17/3.67 fd_pseudo 0
% 20.17/3.67 fd_cond 15
% 20.17/3.67 fd_pseudo_cond 11
% 20.17/3.67 AC symbols 0
% 20.17/3.67
% 20.17/3.67 ------ Input Options Time Limit: Unbounded
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67 ------
% 20.17/3.67 Current options:
% 20.17/3.67 ------
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67 ------ Proving...
% 20.17/3.67
% 20.17/3.67
% 20.17/3.67 % SZS status Theorem for theBenchmark.p
% 20.17/3.67
% 20.17/3.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.17/3.67
% 20.17/3.67
%------------------------------------------------------------------------------