%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM481+3 : 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 : n003.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 02:25:11 PM UTC 2026
% Result : Theorem 19.01s 4.30s
% Output : CNFRefutation 26.10s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f109ERROR: Could not build tree for root c_108646ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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(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(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(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( X1 != sz00
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(f43,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f60,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(f61,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,[],[f60]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f73]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f93]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f99]) ).
fof(f110,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,[],[f69]) ).
fof(f111,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,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f111]) ).
fof(f115,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,[],[f90]) ).
fof(f116,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,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f116]) ).
fof(f124,plain,
! [X6] :
( ~ sP1(X6)
| ( ~ isPrime0(X6)
& ( ? [X8] :
( doDivides0(X8,X6)
& ? [X9] :
( sdtasdt0(X8,X9) = X6
& aNaturalNumber0(X9) )
& aNaturalNumber0(X8)
& X6 != X8
& sz10 != X8 )
| sz10 = X6
| sz00 = X6 ) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f125,plain,
! [X0] :
( ~ sP1(X0)
| ( ~ isPrime0(X0)
& ( ? [X1] :
( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ sP1(X0)
| ( ~ isPrime0(X0)
& ( ( doDivides0(sK5(X0),X0)
& sdtasdt0(sK5(X0),sK6(X0)) = X0
& aNaturalNumber0(sK6(X0))
& aNaturalNumber0(sK5(X0))
& sK5(X0) != X0
& sz10 != sK5(X0) )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f125]) ).
fof(f129,plain,
? [X0] :
( X0 != sz10
& X0 != sz00
& aNaturalNumber0(X0)
& ! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,X0)
| ? [X4] :
( isPrime0(X4)
& sP0(X4)
& sz10 != X4
& sz00 != X4
& doDivides0(X4,X3)
& ? [X5] :
( sdtasdt0(X4,X5) = X3
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) ) )
& ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,X0)
& ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) ) ),
inference(rectify,[],[f109]) ).
fof(f130,plain,
( sz10 != sK7
& sz00 != sK7
& aNaturalNumber0(sK7)
& ! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,sK7)
| ( isPrime0(sK8(X3))
& sP0(sK8(X3))
& sz10 != sK8(X3)
& sz00 != sK8(X3)
& doDivides0(sK8(X3),X3)
& sdtasdt0(sK8(X3),sK9(X3)) = X3
& aNaturalNumber0(sK9(X3))
& aNaturalNumber0(sK8(X3)) ) )
& ! [X1] :
( sP1(X1)
| ( ~ doDivides0(X1,sK7)
& ! [X2] :
( sdtasdt0(X1,X2) != sK7
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X4,sK8(X3)),skolemize(X5,sK9(X3))],[f129]) ).
fof(f131,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f132,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f133,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f134,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f135,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f138,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f139,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f143,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f145,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f57]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f152,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f162,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f177,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f187,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f196,plain,
! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f197,plain,
! [X0] :
( ~ sP1(X0)
| doDivides0(sK5(X0),X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f198,plain,
! [X0] :
( ~ sP1(X0)
| sdtasdt0(sK5(X0),sK6(X0)) = X0
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
! [X0] :
( ~ sP1(X0)
| aNaturalNumber0(sK5(X0))
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f201,plain,
! [X0] :
( ~ sP1(X0)
| sK5(X0) != X0
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f202,plain,
! [X0] :
( ~ sP1(X0)
| sz10 != sK5(X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f205,plain,
sz10 != sK7,
inference(cnf_transformation,[],[f130]) ).
fof(f206,plain,
sz00 != sK7,
inference(cnf_transformation,[],[f130]) ).
fof(f207,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f130]) ).
fof(f208,plain,
! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,sK7)
| isPrime0(sK8(X3)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f213,plain,
! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,sK7)
| sdtasdt0(sK8(X3),sK9(X3)) = X3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f214,plain,
! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,sK7)
| aNaturalNumber0(sK9(X3)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f215,plain,
! [X3] :
( sz10 = X3
| sz00 = X3
| ~ aNaturalNumber0(X3)
| ~ iLess0(X3,sK7)
| aNaturalNumber0(sK8(X3)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f216,plain,
! [X1] :
( sP1(X1)
| ~ doDivides0(X1,sK7)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f217,plain,
! [X2,X1] :
( sP1(X1)
| sdtasdt0(X1,X2) != sK7
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f218,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f157]) ).
fof(f224,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f180]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f131]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f133]) ).
tcf(c_51,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f132]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_113,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( X0 = sz00 )
| ~ sP1(X0)
| ( sK5(X0) != sz10 ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_114,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( X0 = sz00 )
| ~ sP1(X0)
| ( sK5(X0) != X0 ) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_115,plain,
! [X0: $i] :
( aNaturalNumber0(sK5(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ( X0 = sz00 )
| ( sdtasdt0(sK5(X0),sK6(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_118,plain,
! [X0: $i] :
( doDivides0(sK5(X0),X0)
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_119,plain,
! [X0: $i] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_122,negated_conjecture,
! [X0: $i,X1: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sK7 ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_123,negated_conjecture,
! [X0: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK7) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_124,negated_conjecture,
! [X0: $i] :
( aNaturalNumber0(sK8(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_125,negated_conjecture,
! [X0: $i] :
( aNaturalNumber0(sK9(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_126,negated_conjecture,
! [X0: $i] :
( ( X0 = sz10 )
| ( X0 = sz00 )
| ( sdtasdt0(sK8(X0),sK9(X0)) = X0 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_131,negated_conjecture,
! [X0: $i] :
( isPrime0(sK8(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_132,negated_conjecture,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f207]) ).
tcf(c_133,negated_conjecture,
sz00 != sK7,
inference(cnf_transformation,[],[f206]) ).
tcf(c_134,negated_conjecture,
sz10 != sK7,
inference(cnf_transformation,[],[f205]) ).
tcf(c_141,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_198,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_201,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_4670,negated_conjecture,
sz10 != sK7,
inference(demodulation,[status(thm)],[c_134]) ).
tcf(c_4671,negated_conjecture,
sz00 != sK7,
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_4672,negated_conjecture,
aNaturalNumber0(sK7),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_4673,negated_conjecture,
! [X0: $i] :
( isPrime0(sK8(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_4678,negated_conjecture,
! [X0: $i] :
( ( X0 = sz10 )
| ( X0 = sz00 )
| ( sdtasdt0(sK8(X0),sK9(X0)) = X0 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_4679,negated_conjecture,
! [X0: $i] :
( aNaturalNumber0(sK9(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(demodulation,[status(thm)],[c_125]) ).
tcf(c_4680,negated_conjecture,
! [X0: $i] :
( aNaturalNumber0(sK8(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,sK7) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_4681,negated_conjecture,
! [X0: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK7) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_4682,negated_conjecture,
! [X0: $i,X1: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sK7 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_4683,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_4685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6197,plain,
sdtpldt0(sK7,sz00) = sK7,
inference(superposition,[status(thm)],[c_4672,c_56]) ).
tcf(c_6270,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(superposition,[status(thm)],[c_49,c_60]) ).
tcf(c_6272,plain,
sdtasdt0(sK7,sz10) = sK7,
inference(superposition,[status(thm)],[c_4672,c_60]) ).
tcf(c_6287,plain,
( doDivides0(sz00,sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_6270,c_198]) ).
tcf(c_6289,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_6287,c_50,c_49]) ).
tcf(c_6291,plain,
( sP1(sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_6272,c_4682]) ).
tcf(c_6292,plain,
sP1(sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_6291,c_4672,c_50]) ).
tcf(c_6438,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_6441,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK7) = sdtpldt0(sK7,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4672,c_54]) ).
tcf(c_6691,plain,
sdtpldt0(sz10,sK7) = sdtpldt0(sK7,sz10),
inference(superposition,[status(thm)],[c_4672,c_6438]) ).
tcf(c_6712,plain,
( sdtlseqdt0(sK7,sdtpldt0(sz10,sK7))
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_6691,c_201]) ).
tcf(c_6713,plain,
( aNaturalNumber0(sdtpldt0(sz10,sK7))
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_6691,c_52]) ).
tcf(c_6714,plain,
aNaturalNumber0(sdtpldt0(sz10,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_6713,c_4672,c_50]) ).
tcf(c_6715,plain,
sdtlseqdt0(sK7,sdtpldt0(sz10,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_6712,c_4672,c_50]) ).
tcf(c_6724,plain,
sdtasdt0(sdtpldt0(sz10,sK7),sz00) = sz00,
inference(superposition,[status(thm)],[c_6714,c_62]) ).
tcf(c_6726,plain,
sdtasdt0(sdtpldt0(sz10,sK7),sz10) = sdtpldt0(sz10,sK7),
inference(superposition,[status(thm)],[c_6714,c_60]) ).
tcf(c_6741,plain,
! [X0: $i] :
( ( sz00 = sK7 )
| ( sK7 != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_4685]) ).
tcf(c_6742,plain,
( ( sz00 = sK7 )
| ( sK7 != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_6741]) ).
tcf(c_6743,plain,
! [X0: $i] :
( ( sz10 = sK7 )
| ( sK7 != X0 )
| ( sz10 != X0 ) ),
inference(instantiation,[status(thm)],[c_4685]) ).
tcf(c_6869,plain,
( doDivides0(sdtpldt0(sz10,sK7),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7)) ),
inference(superposition,[status(thm)],[c_6724,c_198]) ).
tcf(c_6871,plain,
doDivides0(sdtpldt0(sz10,sK7),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_6869,c_49,c_6714]) ).
tcf(c_7071,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,sK7)
| ~ doDivides0(X0,X1) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_7245,plain,
( doDivides0(sK5(sK7),sK7)
| ( sK7 = sz10 )
| ( sK7 = sz00 )
| ~ sP1(sK7) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_7246,plain,
( ( sK7 = sz10 )
| ( sK7 = sz00 )
| ~ sP1(sK7)
| ( sK5(sK7) != sK7 ) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_7251,plain,
( aNaturalNumber0(sK5(sK7))
| ( sK7 = sz10 )
| ( sK7 = sz00 )
| ~ sP1(sK7) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_7252,plain,
( ( sK7 = sz10 )
| ( sK7 = sz00 )
| ~ sP1(sK7)
| ( sK5(sK7) != sz10 ) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_7293,plain,
( doDivides0(sdtpldt0(sz10,sK7),sdtpldt0(sz10,sK7))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7)) ),
inference(superposition,[status(thm)],[c_6726,c_198]) ).
tcf(c_7296,plain,
doDivides0(sdtpldt0(sz10,sK7),sdtpldt0(sz10,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_7293,c_50,c_6714]) ).
tcf(c_7313,plain,
( sP1(sK5(sK7))
| ( sz10 = sK7 )
| ( sz00 = sK7 )
| ~ sP1(sK7)
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_118,c_4681]) ).
tcf(c_7314,plain,
( sP1(sK5(sK7))
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7313,c_4670,c_4671,c_6292]) ).
tcf(c_7453,plain,
( sP1(sK5(sK7))
| ( sz10 = sK7 )
| ( sz00 = sK7 )
| ~ sP1(sK7) ),
inference(superposition,[status(thm)],[c_115,c_7314]) ).
tcf(c_7454,plain,
sP1(sK5(sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_7453,c_4670,c_4671,c_6292]) ).
tcf(c_8091,plain,
( ( sz10 = sK7 )
| ( sK7 != sz10 )
| ( sz10 != sz10 ) ),
inference(instantiation,[status(thm)],[c_6743]) ).
tcf(c_8092,plain,
sz10 = sz10,
inference(instantiation,[status(thm)],[c_4683]) ).
tcf(c_8122,plain,
( ( sdtpldt0(sz10,sK7) = sK7 )
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7))
| ~ sdtlseqdt0(sdtpldt0(sz10,sK7),sK7) ),
inference(superposition,[status(thm)],[c_6715,c_80]) ).
tcf(c_8142,plain,
( ( sdtpldt0(sz10,sK7) = sK7 )
| ~ sdtlseqdt0(sdtpldt0(sz10,sK7),sK7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8122,c_4672,c_6714]) ).
tcf(c_9075,plain,
( ( sz10 = sK7 )
| ( sz00 = sK7 )
| ( sdtasdt0(sK5(sK7),sK6(sK7)) = sK7 ) ),
inference(superposition,[status(thm)],[c_6292,c_117]) ).
tcf(c_9077,plain,
( ( sK5(sK7) = sz10 )
| ( sK5(sK7) = sz00 )
| ( sdtasdt0(sK5(sK5(sK7)),sK6(sK5(sK7))) = sK5(sK7) ) ),
inference(superposition,[status(thm)],[c_7454,c_117]) ).
tcf(c_9079,plain,
sdtasdt0(sK5(sK7),sK6(sK7)) = sK7,
inference(forward_subsumption_resolution,[status(thm)],[c_9075,c_4670,c_4671]) ).
tcf(c_9350,plain,
( doDivides0(sK5(sK7),sK7)
| ~ aNaturalNumber0(sK6(sK7))
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_9079,c_198]) ).
tcf(c_9786,plain,
! [X0: $i] :
( doDivides0(X0,sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK5(sK7))
| ~ doDivides0(sK5(sK7),sK7)
| ~ doDivides0(X0,sK5(sK7)) ),
inference(instantiation,[status(thm)],[c_7071]) ).
tcf(c_9787,plain,
( doDivides0(sz00,sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK5(sK7))
| ~ doDivides0(sz00,sK5(sK7))
| ~ doDivides0(sK5(sK7),sK7) ),
inference(instantiation,[status(thm)],[c_9786]) ).
tcf(c_9797,plain,
( iLess0(sK5(sK7),sK7)
| ( sK5(sK7) = sK7 )
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sK5(sK7))
| ~ sdtlseqdt0(sK5(sK7),sK7) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_9841,plain,
! [X0: $i] :
( doDivides0(sdtpldt0(sz10,sK7),X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7)) ),
inference(superposition,[status(thm)],[c_6871,c_101]) ).
tcf(c_9862,plain,
! [X0: $i] :
( doDivides0(sdtpldt0(sz10,sK7),X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9841,c_49,c_6714]) ).
tcf(c_10663,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sK7,X0) != sK7 ) ),
inference(superposition,[status(thm)],[c_6197,c_66]) ).
tcf(c_10696,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sK7,X0) != sK7 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10663,c_4672,c_49]) ).
tcf(c_11912,plain,
( doDivides0(sdtpldt0(sz10,sK7),sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7))
| ~ doDivides0(sdtpldt0(sz10,sK7),sz10) ),
inference(superposition,[status(thm)],[c_7296,c_103]) ).
tcf(c_11920,plain,
! [X0: $i] :
( doDivides0(X0,sz10)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK7)
| ~ doDivides0(X0,sdtpldt0(sz10,sK7)) ),
inference(superposition,[status(thm)],[c_6691,c_103]) ).
tcf(c_11974,plain,
! [X0: $i] :
( doDivides0(X0,sz10)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK7)
| ~ doDivides0(X0,sdtpldt0(sz10,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11920,c_4672,c_50]) ).
tcf(c_11979,plain,
( doDivides0(sdtpldt0(sz10,sK7),sK7)
| ~ doDivides0(sdtpldt0(sz10,sK7),sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11912,c_4672,c_50,c_6714]) ).
tcf(c_14391,plain,
( ( sz00 = sz10 )
| ~ aNaturalNumber0(sz10)
| ( sdtpldt0(sz10,sK7) != sK7 ) ),
inference(superposition,[status(thm)],[c_6691,c_10696]) ).
tcf(c_14396,plain,
sdtpldt0(sz10,sK7) != sK7,
inference(forward_subsumption_resolution,[status(thm)],[c_14391,c_51,c_50]) ).
tcf(c_14397,plain,
~ sdtlseqdt0(sdtpldt0(sz10,sK7),sK7),
inference(backward_subsumption_resolution,[status(thm)],[c_8142,c_14396]) ).
tcf(c_19196,plain,
( doDivides0(sdtpldt0(sz10,sK7),sz10)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7))
| ~ doDivides0(sdtpldt0(sz10,sK7),sK7) ),
inference(superposition,[status(thm)],[c_7296,c_11974]) ).
tcf(c_19198,plain,
( doDivides0(sdtpldt0(sz10,sK7),sz10)
| ~ doDivides0(sdtpldt0(sz10,sK7),sK7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19196,c_6714]) ).
tcf(c_27670,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X1,sK5(sK7))
| ~ doDivides0(X2,X0)
| ( X1 != X2 )
| ( sK5(sK7) != X0 ) ),
inference(instantiation,[status(thm)],[c_4692]) ).
tcf(c_27671,plain,
( doDivides0(sz00,sK5(sK7))
| ~ doDivides0(sz00,sz00)
| ( sz00 != sz00 )
| ( sK5(sK7) != sz00 ) ),
inference(instantiation,[status(thm)],[c_27670]) ).
tcf(c_29788,plain,
doDivides0(sK5(sK7),sK7),
inference(global_subsumption_just,[status(thm)],[c_9350,c_49,c_134,c_133,c_141,c_162,c_6292,c_6742,c_7245,c_8091,c_8092]) ).
tcf(c_29796,plain,
( sdtlseqdt0(sK5(sK7),sK7)
| ( sz00 = sK7 )
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29788,c_104]) ).
tcf(c_29799,plain,
( sdtlseqdt0(sK5(sK7),sK7)
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29796,c_4671,c_4672]) ).
tcf(c_29838,plain,
sdtlseqdt0(sK5(sK7),sK7),
inference(global_subsumption_just,[status(thm)],[c_29799,c_49,c_134,c_133,c_141,c_162,c_6292,c_6742,c_7251,c_8091,c_8092,c_29799]) ).
tcf(c_29844,plain,
( iLess0(sK5(sK7),sK7)
| ( sK5(sK7) = sK7 )
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29838,c_94]) ).
tcf(c_29845,plain,
( iLess0(sK5(sK7),sK7)
| ( sK5(sK7) = sK7 )
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29844,c_4672]) ).
tcf(c_29967,plain,
iLess0(sK5(sK7),sK7),
inference(global_subsumption_just,[status(thm)],[c_29845,c_132,c_49,c_134,c_133,c_141,c_162,c_6292,c_6742,c_7251,c_7246,c_8091,c_8092,c_9797,c_29799]) ).
tcf(c_29969,plain,
( ( sK5(sK7) = sz10 )
| ( sK5(sK7) = sz00 )
| ( sdtasdt0(sK8(sK5(sK7)),sK9(sK5(sK7))) = sK5(sK7) )
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29967,c_4678]) ).
tcf(c_29970,plain,
( aNaturalNumber0(sK8(sK5(sK7)))
| ( sK5(sK7) = sz10 )
| ( sK5(sK7) = sz00 )
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29967,c_4680]) ).
tcf(c_29971,plain,
( aNaturalNumber0(sK9(sK5(sK7)))
| ( sK5(sK7) = sz10 )
| ( sK5(sK7) = sz00 )
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29967,c_4679]) ).
tcf(c_29973,plain,
( isPrime0(sK8(sK5(sK7)))
| ( sK5(sK7) = sz10 )
| ( sK5(sK7) = sz00 )
| ~ aNaturalNumber0(sK5(sK7)) ),
inference(superposition,[status(thm)],[c_29967,c_4673]) ).
tcf(c_30558,plain,
( doDivides0(sdtpldt0(sz10,sK7),sz10)
| ~ aNaturalNumber0(sK7)
| ~ doDivides0(sz00,sK7) ),
inference(superposition,[status(thm)],[c_9862,c_19198]) ).
tcf(c_30559,plain,
( doDivides0(sdtpldt0(sz10,sK7),sz10)
| ~ doDivides0(sz00,sK7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30558,c_4672]) ).
tcf(c_30841,plain,
( doDivides0(sdtpldt0(sz10,sK7),sK7)
| ~ doDivides0(sz00,sK7) ),
inference(superposition,[status(thm)],[c_30559,c_11979]) ).
tcf(c_30879,plain,
( sdtlseqdt0(sdtpldt0(sz10,sK7),sK7)
| ( sz00 = sK7 )
| ~ aNaturalNumber0(sK7)
| ~ doDivides0(sz00,sK7)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK7)) ),
inference(superposition,[status(thm)],[c_30841,c_104]) ).
tcf(c_30884,plain,
~ doDivides0(sz00,sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_30879,c_14397,c_4671,c_4672,c_6714]) ).
tcf(c_30885,plain,
aNaturalNumber0(sK8(sK5(sK7))),
inference(global_subsumption_just,[status(thm)],[c_29970,c_132,c_49,c_134,c_133,c_141,c_162,c_6289,c_6292,c_6742,c_7252,c_7251,c_7245,c_8091,c_8092,c_9787,c_27671,c_29970,c_30884]) ).
tcf(c_31027,plain,
aNaturalNumber0(sK9(sK5(sK7))),
inference(global_subsumption_just,[status(thm)],[c_29971,c_132,c_49,c_134,c_133,c_141,c_162,c_6289,c_6292,c_6742,c_7252,c_7251,c_7245,c_8091,c_8092,c_9787,c_27671,c_29971,c_30884]) ).
tcf(c_31139,plain,
isPrime0(sK8(sK5(sK7))),
inference(global_subsumption_just,[status(thm)],[c_29973,c_132,c_49,c_134,c_133,c_141,c_162,c_6289,c_6292,c_6742,c_7252,c_7251,c_7245,c_8091,c_8092,c_9787,c_27671,c_29973,c_30884]) ).
tcf(c_31141,plain,
~ sP1(sK8(sK5(sK7))),
inference(superposition,[status(thm)],[c_31139,c_119]) ).
tcf(c_68304,plain,
sdtasdt0(sK5(sK5(sK7)),sK6(sK5(sK7))) = sK5(sK7),
inference(global_subsumption_just,[status(thm)],[c_9077,c_132,c_49,c_134,c_133,c_141,c_162,c_6289,c_6292,c_6742,c_7252,c_7251,c_7245,c_8091,c_8092,c_9077,c_9787,c_27671,c_30884]) ).
tcf(c_68310,plain,
( aNaturalNumber0(sK5(sK7))
| ~ aNaturalNumber0(sK6(sK5(sK7)))
| ~ aNaturalNumber0(sK5(sK5(sK7))) ),
inference(superposition,[status(thm)],[c_68304,c_53]) ).
tcf(c_78399,plain,
aNaturalNumber0(sK5(sK7)),
inference(global_subsumption_just,[status(thm)],[c_68310,c_49,c_134,c_133,c_141,c_162,c_6292,c_6742,c_7251,c_8091,c_8092]) ).
tcf(c_78438,plain,
sdtpldt0(sK5(sK7),sK7) = sdtpldt0(sK7,sK5(sK7)),
inference(superposition,[status(thm)],[c_78399,c_6441]) ).
tcf(c_86489,plain,
! [X0: $i] :
( doDivides0(X0,sK7)
| ~ aNaturalNumber0(sK7)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK5(sK7))
| ~ doDivides0(X0,sK5(sK7))
| ~ doDivides0(X0,sdtpldt0(sK7,sK5(sK7))) ),
inference(superposition,[status(thm)],[c_78438,c_103]) ).
tcf(c_86555,plain,
! [X0: $i] :
( doDivides0(X0,sK7)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK5(sK7))
| ~ doDivides0(X0,sdtpldt0(sK7,sK5(sK7))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86489,c_4672,c_78399]) ).
tcf(c_87304,plain,
! [X0: $i] :
( doDivides0(X0,sK7)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sK5(sK7)) ),
inference(global_subsumption_just,[status(thm)],[c_86555,c_132,c_49,c_134,c_133,c_141,c_162,c_6292,c_6742,c_7251,c_7245,c_8091,c_8092,c_9786]) ).
tcf(c_106399,plain,
sdtasdt0(sK8(sK5(sK7)),sK9(sK5(sK7))) = sK5(sK7),
inference(global_subsumption_just,[status(thm)],[c_29969,c_132,c_49,c_134,c_133,c_141,c_162,c_6289,c_6292,c_6742,c_7252,c_7251,c_7245,c_8091,c_8092,c_9787,c_27671,c_29969,c_30884]) ).
tcf(c_106406,plain,
( doDivides0(sK8(sK5(sK7)),sK5(sK7))
| ~ aNaturalNumber0(sK9(sK5(sK7)))
| ~ aNaturalNumber0(sK8(sK5(sK7))) ),
inference(superposition,[status(thm)],[c_106399,c_198]) ).
tcf(c_106415,plain,
doDivides0(sK8(sK5(sK7)),sK5(sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_106406,c_31027,c_30885]) ).
tcf(c_108581,plain,
( doDivides0(sK8(sK5(sK7)),sK7)
| ~ aNaturalNumber0(sK8(sK5(sK7))) ),
inference(superposition,[status(thm)],[c_106415,c_87304]) ).
tcf(c_108583,plain,
doDivides0(sK8(sK5(sK7)),sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_108581,c_30885]) ).
tcf(c_108644,plain,
( sP1(sK8(sK5(sK7)))
| ~ aNaturalNumber0(sK8(sK5(sK7))) ),
inference(superposition,[status(thm)],[c_108583,c_4681]) ).
tcf(c_108646,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_108644,c_31141,c_30885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM481+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 04:13:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 19.01/4.30 % SZS status Started for theBenchmark.p
% 19.01/4.30 % SZS status Theorem for theBenchmark.p
% 19.01/4.30
% 19.01/4.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.01/4.30
% 19.01/4.30 % ------ iProver source info
% 19.01/4.30
% 19.01/4.30 % git: date: 2026-07-19 20:42:38 +0200
% 19.01/4.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.01/4.30 % git: non_committed_changes: false
% 19.01/4.30
% 19.01/4.30 % ------ Parsing...
% 19.01/4.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.01/4.30
% 19.01/4.30 % ------ 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 %
% 19.01/4.30
% 19.01/4.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 19.01/4.30
% 19.01/4.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 19.01/4.30 % ------ Proving...
% 19.01/4.30 % ------ Problem Properties
% 19.01/4.30
% 19.01/4.30 %
% 19.01/4.30 % clauses 81
% 19.01/4.30 % conjectures 13
% 19.01/4.30 % EPR 20
% 19.01/4.30 % Horn 44
% 19.01/4.30 % unary 8
% 19.01/4.30 % binary 8
% 19.01/4.30 % lits 324
% 19.01/4.30 % lits eq 106
% 19.01/4.30 % fd_pure 0
% 19.01/4.30 % fd_pseudo 0
% 19.01/4.30 % fd_cond 24
% 19.01/4.30 % fd_pseudo_cond 12
% 19.01/4.30 % AC symbols 0
% 19.01/4.30
% 19.01/4.30 % ------ Schedule dynamic 5 is on
% 19.01/4.30
% 19.01/4.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.01/4.30
% 19.01/4.30
% 19.01/4.30 % ------
% 19.01/4.30 % Current options:
% 19.01/4.30 % ------
% 19.01/4.30
% 19.01/4.30
% 19.01/4.30 %
% 19.01/4.30
% 19.01/4.30 % ------ Proving...
% 19.01/4.30 %
% 19.01/4.30
% 19.01/4.30 % SZS status Theorem for theBenchmark.p
% 19.01/4.30
% 19.01/4.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.10/4.30
% 26.10/4.30
%------------------------------------------------------------------------------