%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM487+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 : n001.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 02:25:13 PM UTC 2026
% Result : Theorem 15.81s 3.24s
% Output : CNFRefutation 15.81s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f219ERROR: Could not build tree for root c_31038ERROR: 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(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(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
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(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f44,conjecture,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f48]) ).
fof(f56,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f65]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f75]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(flattening,[],[f84]) ).
fof(f108,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(f109,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f108]) ).
fof(f114,plain,
( ~ sdtlseqdt0(xr,xn)
| xn = xr ),
inference(ennf_transformation,[],[f45]) ).
fof(f115,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,[],[f74]) ).
fof(f116,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,[],[f115]) ).
fof(f117,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))],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f119,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(flattening,[],[f118]) ).
fof(f125,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,[],[f109]) ).
fof(f126,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,[],[f125]) ).
fof(f127,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,[],[f126]) ).
fof(f128,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))],[f127]) ).
fof(f130,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f137,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f190,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f128]) ).
fof(f198,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f200,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f203,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f204,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f205,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f206,plain,
( ~ sdtlseqdt0(xr,xn)
| xn = xr ),
inference(cnf_transformation,[],[f114]) ).
fof(f207,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f156]) ).
fof(f209,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f158]) ).
fof(f210,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f157]) ).
fof(f217,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f190]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f130]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f210]) ).
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,[],[f162]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f200]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f198]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f203]) ).
tcf(c_122,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f204]) ).
tcf(c_123,plain,
sdtmndt0(xn,xp) = xr,
inference(cnf_transformation,[],[f205]) ).
tcf(c_124,negated_conjecture,
( ( xn = xr )
| ~ sdtlseqdt0(xr,xn) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_170,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).
tcf(c_175,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_1043,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_170,c_120]) ).
tcf(c_2341,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2343,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2344,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3563,plain,
! [X0: $i] :
( sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_3567,plain,
! [X0: $i] :
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ( xr != X0 ) ),
inference(instantiation,[status(thm)],[c_2344]) ).
tcf(c_3592,plain,
! [X0: $i,X1: $i] :
( ( xr = X0 )
| ( xr != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2343]) ).
tcf(c_3628,plain,
! [X0: $i] :
( ( xr = X0 )
| ( xr != xr )
| ( X0 != xr ) ),
inference(instantiation,[status(thm)],[c_3592]) ).
tcf(c_3675,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xr != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2347]) ).
tcf(c_3692,plain,
xr = xr,
inference(instantiation,[status(thm)],[c_2341]) ).
tcf(c_3854,plain,
( ( xr = sdtmndt0(xn,xp) )
| ( xr != xr )
| ( sdtmndt0(xn,xp) != xr ) ),
inference(instantiation,[status(thm)],[c_3628]) ).
tcf(c_3962,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( xr != sdtmndt0(xn,xp) ) ),
inference(instantiation,[status(thm)],[c_3567]) ).
tcf(c_3969,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),X1)
| ( xr != sdtmndt0(xn,xp) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3675]) ).
tcf(c_4056,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_4152,plain,
! [X0: $i] :
( sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),sdtmndt0(xn,xp))
| ( xr != sdtmndt0(xn,xp) )
| ( X0 != sdtmndt0(xn,xp) ) ),
inference(instantiation,[status(thm)],[c_3969]) ).
tcf(c_4490,plain,
( ( sdtpldt0(sz00,sdtmndt0(xn,xp)) = sdtmndt0(xn,xp) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_4840,plain,
sdtpldt0(sz00,xp) = xp,
inference(superposition,[status(thm)],[c_118,c_57]) ).
tcf(c_4848,plain,
( sdtlseqdt0(sdtmndt0(xn,xp),sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_5522,plain,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4840,c_175]) ).
tcf(c_6618,plain,
( sdtlseqdt0(xr,sdtpldt0(sz00,sdtmndt0(xn,xp)))
| ~ sdtlseqdt0(sdtmndt0(xn,xp),sdtmndt0(xn,xp))
| ( xr != sdtmndt0(xn,xp) )
| ( sdtpldt0(sz00,sdtmndt0(xn,xp)) != sdtmndt0(xn,xp) ) ),
inference(instantiation,[status(thm)],[c_4152]) ).
tcf(c_7027,plain,
! [X0: $i] :
( ( xn = X0 )
| ~ sdtlseqdt0(xr,xn)
| ( X0 != xr ) ),
inference(resolution,[status(thm)],[c_2343,c_124]) ).
tcf(c_7029,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2343,c_2341]) ).
tcf(c_7461,plain,
( ( xn = sdtpldt0(sz00,xr) )
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xr,xn) ),
inference(resolution,[status(thm)],[c_7027,c_57]) ).
tcf(c_7887,plain,
( ( xn = sdtpldt0(sz00,xr) )
| ~ sdtlseqdt0(xr,xn) ),
inference(global_subsumption_just,[status(thm)],[c_7461,c_118,c_116,c_122,c_123,c_3692,c_3854,c_3962,c_4056,c_7461]) ).
tcf(c_8834,plain,
( aNaturalNumber0(sdtpldt0(sz00,sdtmndt0(xn,xp)))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_11051,plain,
( ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_122,c_78]) ).
tcf(c_13750,plain,
( ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_122,c_78]) ).
tcf(c_16046,plain,
( sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(sz00,sdtmndt0(xn,xp)))
| ~ sdtlseqdt0(xr,sdtpldt0(sz00,sdtmndt0(xn,xp)))
| ~ sdtlseqdt0(sdtpldt0(sz00,sdtmndt0(xn,xp)),xn) ),
inference(instantiation,[status(thm)],[c_3563]) ).
tcf(c_17232,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(global_subsumption_just,[status(thm)],[c_13750,c_118,c_116,c_11051]) ).
tcf(c_19407,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(X0,sdtmndt0(xn,xp)),xn)
| ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(superposition,[status(thm)],[c_17232,c_87]) ).
tcf(c_19421,plain,
( sdtlseqdt0(sdtpldt0(sz00,sdtmndt0(xn,xp)),xn)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(instantiation,[status(thm)],[c_19407]) ).
tcf(c_24607,plain,
( ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_122,c_78]) ).
tcf(c_28930,plain,
( ( sdtpldt0(sz00,xr) = xn )
| ~ sdtlseqdt0(xr,xn) ),
inference(resolution,[status(thm)],[c_7029,c_7887]) ).
tcf(c_29974,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(global_subsumption_just,[status(thm)],[c_24607,c_118,c_116,c_11051]) ).
tcf(c_29976,plain,
sdtpldt0(xp,xr) = xn,
inference(superposition,[status(thm)],[c_123,c_29974]) ).
tcf(c_31033,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xr) != xn ) ),
inference(superposition,[status(thm)],[c_29976,c_67]) ).
tcf(c_31037,plain,
( ( sz00 = xp )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,xr) != xn ) ),
inference(instantiation,[status(thm)],[c_31033]) ).
tcf(c_31038,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_31037,c_28930,c_19421,c_16046,c_8834,c_6618,c_5522,c_4848,c_4490,c_4056,c_3962,c_3854,c_3692,c_1043,c_123,c_122,c_49,c_116,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM487+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 04:20:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 15.81/3.24 % SZS status Started for theBenchmark.p
% 15.81/3.24 % SZS status Theorem for theBenchmark.p
% 15.81/3.24
% 15.81/3.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.81/3.24
% 15.81/3.24 % ------ iProver source info
% 15.81/3.24
% 15.81/3.24 % git: date: 2026-07-19 20:42:38 +0200
% 15.81/3.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.81/3.24 % git: non_committed_changes: false
% 15.81/3.24
% 15.81/3.24 % ------ Parsing...
% 15.81/3.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.81/3.24
% 15.81/3.24 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 15.81/3.24
% 15.81/3.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.81/3.24
% 15.81/3.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.81/3.24 % ------ Proving...
% 15.81/3.24 % ------ Problem Properties
% 15.81/3.24
% 15.81/3.24 %
% 15.81/3.24 % clauses 71
% 15.81/3.24 % conjectures 1
% 15.81/3.24 % EPR 20
% 15.81/3.24 % Horn 46
% 15.81/3.24 % unary 12
% 15.81/3.24 % binary 8
% 15.81/3.24 % lits 267
% 15.81/3.24 % lits eq 73
% 15.81/3.24 % fd_pure 0
% 15.81/3.24 % fd_pseudo 0
% 15.81/3.24 % fd_cond 15
% 15.81/3.24 % fd_pseudo_cond 11
% 15.81/3.24 % AC symbols 0
% 15.81/3.24
% 15.81/3.24 % ------ Input Options Time Limit: Unbounded
% 15.81/3.24
% 15.81/3.24
% 15.81/3.24 % ------
% 15.81/3.24 % Current options:
% 15.81/3.24 % ------
% 15.81/3.24
% 15.81/3.24
% 15.81/3.24 %
% 15.81/3.24
% 15.81/3.24 % ------ Proving...
% 15.81/3.24 %
% 15.81/3.24
% 15.81/3.24 % SZS status Theorem for theBenchmark.p
% 15.81/3.24
% 15.81/3.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.81/3.24
% 15.81/3.24
%------------------------------------------------------------------------------