%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:25:21 PM UTC 2026
% Result : Theorem 56.74s 8.82s
% Output : CNFRefutation 56.74s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f242ERROR: Could not build tree for root c_37663ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& X0 != sz00 )
=> ( 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/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f50,axiom,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox2/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/sandbox2/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,[status(cth)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [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 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f75,plain,
! [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 ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f76]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f80]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [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) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f94,plain,
! [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) ) ),
inference(flattening,[],[f93]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f103]) ).
fof(f115,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f116,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
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] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f124]) ).
fof(f128,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f132,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(nnf_transformation,[],[f116]) ).
fof(f134,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0))
& sK2(X0) != X0
& sz10 != sK2(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f135]) ).
fof(f138,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f142,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f145,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f63]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f151,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f152,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f69]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f159,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f198,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f136]) ).
fof(f206,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f208,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f210,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f211,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f213,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f43]) ).
fof(f216,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f217,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f218,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f222,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f228,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f50]) ).
fof(f229,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(f230,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f164]) ).
fof(f236,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f187]) ).
fof(f238,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f189]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f188]) ).
fof(f240,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f198]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f138]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1) ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f208]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f207]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f206]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f211]) ).
tcf(c_121,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f210]) ).
tcf(c_123,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f213]) ).
tcf(c_124,plain,
xn != xp,
inference(cnf_transformation,[],[f217]) ).
tcf(c_125,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f216]) ).
tcf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f218]) ).
tcf(c_131,plain,
sz00 != xk,
inference(cnf_transformation,[],[f222]) ).
tcf(c_138,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f228]) ).
tcf(c_139,negated_conjecture,
( ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_140,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_144,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_162,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_185,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_1600,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_185,c_120]) ).
tcf(c_3560,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4851,plain,
! [X0: $i] :
( ( sz00 = xk )
| ( xk != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_3562]) ).
tcf(c_4852,plain,
( ( sz00 = xk )
| ( xk != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_4851]) ).
tcf(c_4878,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,X1)
| ( sdtasdt0(xp,xk) != X1 )
| ( sdtasdt0(xp,xm) != X0 ) ),
inference(instantiation,[status(thm)],[c_3566]) ).
tcf(c_4907,plain,
! [X0: $i] :
( sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_4979,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5027,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ( sdtasdt0(xp,xk) != sdtasdt0(xp,xk) )
| ( sdtasdt0(xp,xm) != X0 ) ),
inference(instantiation,[status(thm)],[c_4878]) ).
tcf(c_5028,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,xk),
inference(instantiation,[status(thm)],[c_3560]) ).
tcf(c_5030,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xp,xk) = X1 )
| ( X1 != X0 )
| ( sdtasdt0(xp,xk) != X0 ) ),
inference(instantiation,[status(thm)],[c_3562]) ).
tcf(c_5041,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_5178,plain,
! [X0: $i,X1: $i] :
( ( X0 = xp )
| ( xp != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3562]) ).
tcf(c_5179,plain,
( ( sz00 = xp )
| ( xp != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_5178]) ).
tcf(c_5249,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_83,c_139]) ).
tcf(c_5288,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5395,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_5459,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5395,c_187]) ).
tcf(c_5463,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_5459,c_118,c_49]) ).
tcf(c_5550,plain,
! [X0: $i,X1: $i] :
( ( xp = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != sdtasdt0(xp,X1) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_5551,plain,
! [X0: $i] :
( ( xp = sz00 )
| ( sdtasdt0(xp,sdtsldt0(X0,xp)) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_5568,plain,
( ( xp = sz00 )
| ( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ doDivides0(xp,sz00) ),
inference(instantiation,[status(thm)],[c_5551]) ).
tcf(c_6329,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_6923,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xk))
| ( sdtasdt0(xp,xk) != sdtasdt0(xp,xk) )
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xk) ) ),
inference(instantiation,[status(thm)],[c_5027]) ).
tcf(c_6924,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_7802,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_57]) ).
tcf(c_7896,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_7802,c_190]) ).
tcf(c_7910,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_7896,c_117,c_49]) ).
tcf(c_7923,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_83,c_139]) ).
tcf(c_7944,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
tcf(c_7968,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_117,c_7944]) ).
tcf(c_7976,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_7923,c_117,c_116,c_5249,c_5288]) ).
tcf(c_7978,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(light_normalisation,[status(thm)],[c_7976,c_7968]) ).
tcf(c_7989,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_83,c_7978]) ).
tcf(c_8447,plain,
( ( sz00 = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xm,sz00) ),
inference(superposition,[status(thm)],[c_7910,c_80]) ).
tcf(c_8463,plain,
( ( sz00 = xm )
| ~ sdtlseqdt0(xm,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8447,c_117,c_49]) ).
tcf(c_8649,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_128,c_99]) ).
tcf(c_8662,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8649,c_118,c_121]) ).
tcf(c_8892,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(superposition,[status(thm)],[c_7989,c_81]) ).
tcf(c_9018,plain,
( sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xk,xm)
| ~ sdtlseqdt0(xp,xk) ),
inference(instantiation,[status(thm)],[c_4907]) ).
tcf(c_9346,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_8892,c_118,c_117,c_116,c_1600,c_4979,c_5288,c_8662,c_8892]) ).
tcf(c_9347,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(renaming,[status(thm)],[c_9346]) ).
tcf(c_9360,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(superposition,[status(thm)],[c_9347,c_94]) ).
tcf(c_11725,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_83,c_139]) ).
tcf(c_11814,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_11725,c_117,c_116,c_5249,c_5288]) ).
tcf(c_13627,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xp,xk) = sdtasdt0(xp,X0) )
| ( sdtasdt0(xp,xk) != X1 )
| ( sdtasdt0(xp,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_5030]) ).
tcf(c_13628,plain,
! [X0: $i] :
( ( xk = X0 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,xk) != sdtasdt0(xp,X0) ) ),
inference(instantiation,[status(thm)],[c_5550]) ).
tcf(c_13629,plain,
( ( sdtasdt0(xp,xk) = sdtasdt0(xp,sz00) )
| ( sdtasdt0(xp,xk) != sz00 )
| ( sdtasdt0(xp,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_13627]) ).
tcf(c_13630,plain,
( ( xk = sz00 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ( sdtasdt0(xp,xk) != sdtasdt0(xp,sz00) ) ),
inference(instantiation,[status(thm)],[c_13628]) ).
tcf(c_14225,plain,
( sdtlseqdt0(xk,xm)
| sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_6329]) ).
tcf(c_15636,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( xm = xk )
| ( sz00 = xp )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_89,c_11814]) ).
tcf(c_15675,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( xm = xk )
| ( sz00 = xp )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15636,c_118,c_117]) ).
tcf(c_16358,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( xm = xk )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ) ),
inference(global_subsumption_just,[status(thm)],[c_15675,c_118,c_117,c_116,c_138,c_123,c_1600,c_5288,c_8662,c_9018,c_14225,c_15675]) ).
tcf(c_16359,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( xm = xk )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(renaming,[status(thm)],[c_16358]) ).
tcf(c_16367,plain,
( ( xm = xk )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_16359,c_80]) ).
tcf(c_19380,plain,
( ( xp = sz00 )
| ( xm = xk )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c_68,c_139]) ).
tcf(c_20179,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_20185,plain,
sdtasdt0(sz00,xn) = sz00,
inference(superposition,[status(thm)],[c_116,c_63]) ).
tcf(c_20329,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_83,c_139]) ).
tcf(c_20350,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
tcf(c_20351,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_20380,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_117,c_20350]) ).
tcf(c_20394,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(superposition,[status(thm)],[c_118,c_20351]) ).
tcf(c_20396,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_20329,c_117,c_116,c_5249,c_5288]) ).
tcf(c_20398,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(light_normalisation,[status(thm)],[c_20396,c_20380]) ).
tcf(c_20409,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_83,c_20398]) ).
tcf(c_20411,plain,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_20409,c_118,c_117,c_116,c_1600,c_4979,c_5288,c_7989,c_8662]) ).
tcf(c_20611,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_20179,c_187]) ).
tcf(c_20614,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_20611,c_118,c_49]) ).
tcf(c_21031,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(superposition,[status(thm)],[c_20411,c_81]) ).
tcf(c_21108,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_21031,c_118,c_117,c_116,c_1600,c_4979,c_5288,c_8662,c_8892]) ).
tcf(c_21109,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(renaming,[status(thm)],[c_21108]) ).
tcf(c_21121,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(superposition,[status(thm)],[c_21109,c_94]) ).
tcf(c_21150,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_21121,c_118,c_117,c_116,c_1600,c_4979,c_5288,c_8662,c_9360]) ).
tcf(c_21151,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(renaming,[status(thm)],[c_21150]) ).
tcf(c_21575,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_20614,c_100]) ).
tcf(c_21602,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21575,c_118,c_49]) ).
tcf(c_22548,plain,
( ( xn = xp )
| ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_91,c_139]) ).
tcf(c_22594,plain,
( ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22548,c_124,c_118,c_117,c_116,c_125]) ).
tcf(c_22801,plain,
( ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(light_normalisation,[status(thm)],[c_22594,c_20380]) ).
tcf(c_22812,plain,
( ( xm = xk )
| ( sz00 = xp )
| ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,xk) ),
inference(superposition,[status(thm)],[c_89,c_22801]) ).
tcf(c_22813,plain,
( ( xm = xk )
| ( sz00 = xp )
| ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(xm,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22812,c_118,c_117]) ).
tcf(c_22828,plain,
( ( xm = xk )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sz00 = xm ) ),
inference(global_subsumption_just,[status(thm)],[c_22813,c_118,c_117,c_116,c_138,c_123,c_1600,c_5288,c_8662,c_9018,c_14225,c_22813]) ).
tcf(c_22829,plain,
( ( xm = xk )
| ( sz00 = xm )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) ) ),
inference(renaming,[status(thm)],[c_22828]) ).
tcf(c_22855,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xm))
| ( xm = xk )
| ( sz00 = xm )
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(superposition,[status(thm)],[c_22829,c_21151]) ).
tcf(c_22956,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm)],[c_128,c_20380]) ).
tcf(c_23830,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ( xm = xk ) ),
inference(global_subsumption_just,[status(thm)],[c_19380,c_118,c_117,c_116,c_49,c_144,c_162,c_1600,c_5179,c_5288,c_8662,c_19380]) ).
tcf(c_23831,plain,
( ( xm = xk )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(renaming,[status(thm)],[c_23830]) ).
tcf(c_23956,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_20394,c_53]) ).
tcf(c_23964,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_23956,c_118,c_117]) ).
tcf(c_24091,plain,
! [X0: $i] :
( iLess0(sdtasdt0(xp,xk),X0)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xm))
| ( xm = xk )
| ( sz00 = xm )
| ( sdtasdt0(xp,xk) = X0 )
| ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xp,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_22855,c_23964]) ).
tcf(c_24317,plain,
( ( xm = xk )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xm) )
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_23831,c_118,c_117,c_116,c_1600,c_4979,c_5028,c_5288,c_6923,c_6924,c_8662,c_16367,c_23831,c_23964]) ).
tcf(c_24332,plain,
( ( xm = xk )
| ( xm = sz00 )
| ( xn = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c_24317,c_69]) ).
tcf(c_24440,plain,
( ( xm = xk )
| ( xm = sz00 )
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_24332,c_118,c_117,c_116,c_124,c_24332]) ).
tcf(c_24916,plain,
( ( xm = xk )
| ( xm = sz00 )
| ( xn = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xp) ),
inference(resolution,[status(thm)],[c_91,c_24440]) ).
tcf(c_26819,plain,
( ( xm = xk )
| ( xm = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_24916,c_118,c_117,c_116,c_125,c_124,c_24916]) ).
tcf(c_30727,plain,
sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00,
inference(global_subsumption_just,[status(thm)],[c_21602,c_118,c_49,c_144,c_162,c_1600,c_5179,c_5463,c_5568]) ).
tcf(c_32434,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xm,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xm != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3566]) ).
tcf(c_32435,plain,
( sdtlseqdt0(xm,sz00)
| ~ sdtlseqdt0(sz00,sz00)
| ( xm != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_32434]) ).
tcf(c_34993,plain,
( ( xm = xk )
| ( sz00 = xm ) ),
inference(global_subsumption_just,[status(thm)],[c_24091,c_49,c_140,c_144,c_162,c_8463,c_26819,c_32435]) ).
tcf(c_35036,plain,
( sdtlseqdt0(xp,xm)
| ( sz00 = xm ) ),
inference(superposition,[status(thm)],[c_34993,c_138]) ).
tcf(c_35040,plain,
sz00 = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_35036,c_123]) ).
tcf(c_35086,plain,
sdtsldt0(sdtasdt0(sz00,xn),xp) = xk,
inference(demodulation,[status(thm)],[c_22956,c_35040]) ).
tcf(c_37661,plain,
sdtsldt0(sz00,xp) = xk,
inference(light_normalisation,[status(thm)],[c_35086,c_20185]) ).
tcf(c_37662,plain,
sdtasdt0(xp,xk) = sz00,
inference(demodulation,[status(thm)],[c_30727,c_37661]) ).
tcf(c_37663,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_37662,c_13630,c_13629,c_8662,c_5288,c_5179,c_5041,c_4852,c_1600,c_162,c_144,c_131,c_49,c_116,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:19:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 56.74/8.82 % SZS status Started for theBenchmark.p
% 56.74/8.82 % SZS status Theorem for theBenchmark.p
% 56.74/8.82
% 56.74/8.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 56.74/8.82
% 56.74/8.82 % ------ iProver source info
% 56.74/8.82
% 56.74/8.82 % git: date: 2026-07-19 20:42:38 +0200
% 56.74/8.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 56.74/8.82 % git: non_committed_changes: false
% 56.74/8.82
% 56.74/8.82 % ------ Parsing...
% 56.74/8.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 56.74/8.82
% 56.74/8.82 % ------ 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 %
% 56.74/8.82
% 56.74/8.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 56.74/8.82
% 56.74/8.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 56.74/8.82 % ------ Proving...
% 56.74/8.82 % ------ Problem Properties
% 56.74/8.82
% 56.74/8.82 %
% 56.74/8.82 % clauses 84
% 56.74/8.82 % conjectures 1
% 56.74/8.82 % EPR 31
% 56.74/8.82 % Horn 58
% 56.74/8.82 % unary 25
% 56.74/8.82 % binary 7
% 56.74/8.82 % lits 282
% 56.74/8.82 % lits eq 78
% 56.74/8.82 % fd_pure 0
% 56.74/8.82 % fd_pseudo 0
% 56.74/8.82 % fd_cond 15
% 56.74/8.82 % fd_pseudo_cond 11
% 56.74/8.82 % AC symbols 0
% 56.74/8.82
% 56.74/8.82 % ------ Input Options Time Limit: Unbounded
% 56.74/8.82
% 56.74/8.82
% 56.74/8.82 % ------
% 56.74/8.82 % Current options:
% 56.74/8.82 % ------
% 56.74/8.82
% 56.74/8.82
% 56.74/8.82 %
% 56.74/8.82
% 56.74/8.82 % ------ Proving...
% 56.74/8.82 %
% 56.74/8.82
% 56.74/8.82 % SZS status Theorem for theBenchmark.p
% 56.74/8.82
% 56.74/8.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 56.74/8.83
% 56.74/8.83
%------------------------------------------------------------------------------