%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 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 : Thu Sep 24 01:55:16 PM UTC 2026
% Result : Theorem 8.27s 1.58s
% Output : CNFRefutation 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 30
% Syntax : Number of formulae : 177 ( 49 unt; 0 def)
% Number of atoms : 661 ( 247 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 803 ( 319 ~; 330 |; 105 &)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 196 ( 3 sgn 97 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__,conjecture,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__2389,hypothesis,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2389) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(m__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(c_0_30,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
fof(c_0_31,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_32,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_33,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])])]) ).
fof(c_0_34,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])]) ).
cnf(c_0_35,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_39,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_40,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,hypothesis,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_45,hypothesis,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_46,hypothesis,
xp != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
fof(c_0_47,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_49,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| X1 != xk
| sdtasdt0(xm,xn) = sdtasdt0(xp,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_42])]),c_0_46]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| X1 != xk
| aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_44]),c_0_45]),c_0_42])]),c_0_46]) ).
cnf(c_0_52,hypothesis,
( X1 != xk
| sdtasdt0(xm,xn) = sdtasdt0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_37]),c_0_38])]) ).
cnf(c_0_53,hypothesis,
( X1 != xk
| aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_37]),c_0_38])]) ).
fof(c_0_54,plain,
! [X70,X71,X72] :
( doDivides0(X70,X72)
| ~ doDivides0(X71,X72)
| ~ doDivides0(X70,X71)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
cnf(c_0_55,hypothesis,
( X1 != xk
| aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_42])]),c_0_53]) ).
fof(c_0_56,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_57,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_58,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
cnf(c_0_59,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_61,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(er,[status(thm)],[c_0_55]) ).
fof(c_0_64,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_65,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_56]) ).
fof(c_0_66,plain,
! [X28,X29,X30] :
( ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X29,X28) != sdtasdt0(X30,X28) )
& ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X28,X29) != sdtasdt0(X28,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])]) ).
cnf(c_0_67,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_68,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| ~ doDivides0(X1,xr)
| doDivides0(X1,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_70,hypothesis,
aNaturalNumber0(xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_45]),c_0_44]),c_0_42]),c_0_63])]),c_0_46]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_73,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
fof(c_0_74,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(assume_negation,[status(cth)],[m__]) ).
fof(c_0_75,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_78,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(csr,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_80,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xr)
| doDivides0(X1,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_71]),c_0_72])])]) ).
fof(c_0_82,plain,
! [X43,X44] :
( X43 = X44
| ~ sdtlseqdt0(X44,X43)
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_83,plain,
! [X45,X46,X47] :
( sdtlseqdt0(X45,X47)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
fof(c_0_84,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_nnf,[status(thm)],[c_0_73]) ).
fof(c_0_85,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_86,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(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_87,plain,
! [X53,X54,X55] :
( ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X54,X53),sdtasdt0(X55,X53)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X54,X53) != sdtasdt0(X55,X53) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X53,X54),sdtasdt0(X53,X55)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X53,X54) != sdtasdt0(X53,X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X2,X1) != X3
| X2 = sz00
| X1 = esk2_2(X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_68]) ).
cnf(c_0_89,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_90,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| esk2_2(X1,X2) = sdtsldt0(X2,X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_77])]),c_0_78]) ).
cnf(c_0_91,hypothesis,
doDivides0(sz10,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_72]),c_0_61])]) ).
cnf(c_0_92,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_93,hypothesis,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2389]) ).
cnf(c_0_94,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_95,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_96,plain,
! [X48,X49] :
( ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| sdtlseqdt0(X49,X48) )
& ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| X49 != X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
fof(c_0_97,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
fof(c_0_98,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
fof(c_0_99,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(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])]) ).
cnf(c_0_100,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_101,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_102,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_103,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_104,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_105,plain,
( ~ aNaturalNumber0(X1)
| esk2_2(sz10,X1) = X1 ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_71]),c_0_72])]),c_0_89])]) ).
cnf(c_0_106,hypothesis,
esk2_2(sz10,xk) = sdtsldt0(xk,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_72]),c_0_70])]),c_0_89]) ).
cnf(c_0_107,hypothesis,
( ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_42])]) ).
cnf(c_0_108,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xm)
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_42]),c_0_38])]) ).
cnf(c_0_109,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_110,plain,
! [X79,X80] :
( sdtlseqdt0(X79,X80)
| X80 = sz00
| ~ doDivides0(X79,X80)
| ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])]) ).
cnf(c_0_111,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_113,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_114,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| X1 = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_42]),c_0_37])]),c_0_102]) ).
cnf(c_0_115,hypothesis,
sdtasdt0(xm,xn) = sdtasdt0(xp,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_45]),c_0_44]),c_0_42]),c_0_63])]),c_0_46]) ).
cnf(c_0_116,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xp))
| X1 = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_95]),c_0_42]),c_0_38])]),c_0_104]) ).
cnf(c_0_117,hypothesis,
sdtsldt0(xk,sz10) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_70])]) ).
cnf(c_0_118,hypothesis,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_70])]) ).
cnf(c_0_119,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xp)
| sdtlseqdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_38])]) ).
cnf(c_0_120,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| X1 != xk
| sdtasdt0(xn,xm) = sdtasdt0(xp,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_39]),c_0_42])]),c_0_46]) ).
cnf(c_0_121,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_122,hypothesis,
doDivides0(xr,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_123,hypothesis,
( X1 != xk
| sdtasdt0(xm,xn) != sz00
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_52]),c_0_42])]),c_0_46]),c_0_53]) ).
fof(c_0_124,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_125,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xp,xm))
| sdtasdt0(xm,xn) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_126,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,xp))
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_38])]) ).
cnf(c_0_127,hypothesis,
sdtlseqdt0(xm,sdtasdt0(sz10,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_71]),c_0_72]),c_0_38])]),c_0_89]) ).
cnf(c_0_128,hypothesis,
( X1 != xk
| sdtasdt0(sz10,X1) = xk ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_117]),c_0_91]),c_0_72]),c_0_70])]),c_0_89]) ).
cnf(c_0_129,hypothesis,
( sdtlseqdt0(xm,xk)
| xk = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_70])]) ).
fof(c_0_130,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_131,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_132,hypothesis,
( X1 != xk
| sdtasdt0(xn,xm) = sdtasdt0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_50]),c_0_38]),c_0_37])]) ).
cnf(c_0_133,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| sdtlseqdt0(xr,sdtasdt0(xm,xn))
| sdtasdt0(xm,xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_61])]) ).
cnf(c_0_134,hypothesis,
( X2 != xk
| X1 != xk
| sdtasdt0(xp,X2) != sz00
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_123,c_0_52]) ).
cnf(c_0_135,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_136,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_115]),c_0_115])]) ).
cnf(c_0_137,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_36]),c_0_42]),c_0_38])]) ).
cnf(c_0_138,hypothesis,
sdtlseqdt0(xm,xk),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_139,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_140,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_141,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_142,hypothesis,
( X1 != xk
| sdtasdt0(xn,xm) = sdtasdt0(xm,xn) ),
inference(spm,[status(thm)],[c_0_52,c_0_132]) ).
cnf(c_0_143,hypothesis,
( sdtlseqdt0(xr,sdtasdt0(xm,xn))
| sdtasdt0(xm,xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_50]),c_0_37]),c_0_38])]) ).
cnf(c_0_144,hypothesis,
( X1 != xk
| sdtasdt0(xp,X1) != sz00 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_134]),c_0_135]) ).
cnf(c_0_145,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| xm = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_146,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtlseqdt0(X3,X2)
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X2 = X3
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_100,c_0_109]) ).
cnf(c_0_147,hypothesis,
( ~ sdtlseqdt0(xk,xm)
| xk = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_138]),c_0_38]),c_0_70])]) ).
cnf(c_0_148,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141])]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(er,[status(thm)],[c_0_142]) ).
fof(c_0_150,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
fof(c_0_151,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])]) ).
cnf(c_0_152,hypothesis,
( X1 != xk
| sdtlseqdt0(xr,sdtasdt0(xp,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_52]),c_0_144]) ).
cnf(c_0_153,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_50]) ).
cnf(c_0_154,negated_conjecture,
( xm = sz00
| xk = xm
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_70]),c_0_38]),c_0_42])]),c_0_46]),c_0_147]) ).
cnf(c_0_155,hypothesis,
( X1 != xk
| sdtsldt0(sdtasdt0(xp,X1),xp) = xk ),
inference(spm,[status(thm)],[c_0_44,c_0_52]) ).
fof(c_0_156,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(sz00,sdtasdt0(xm,xn)) = sdtasdt0(sz00,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_38]),c_0_37])]) ).
cnf(c_0_158,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_159,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_160,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_161,hypothesis,
( X1 != xk
| sdtlseqdt0(xr,sdtasdt0(xm,xn)) ),
inference(spm,[status(thm)],[c_0_152,c_0_52]) ).
cnf(c_0_162,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_163,negated_conjecture,
( xm = sz00
| sdtsldt0(sdtasdt0(xp,xm),xp) = xk ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_42]),c_0_70])]),c_0_46]),c_0_155]) ).
fof(c_0_164,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_nnf,[status(thm)],[c_0_156]) ).
cnf(c_0_165,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_157]),c_0_63])]) ).
cnf(c_0_166,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| X2 != sz00
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_160]) ).
cnf(c_0_167,hypothesis,
sdtlseqdt0(xr,sdtasdt0(xm,xn)),
inference(er,[status(thm)],[c_0_161]) ).
cnf(c_0_168,hypothesis,
xr != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_162]),c_0_61])]) ).
cnf(c_0_169,negated_conjecture,
( xk = xm
| xm = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_163]),c_0_42]),c_0_38])]),c_0_46]) ).
cnf(c_0_170,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_171,hypothesis,
sdtasdt0(sz00,sdtasdt0(xm,xn)) = sz00,
inference(rw,[status(thm)],[c_0_157,c_0_165]) ).
cnf(c_0_172,hypothesis,
sdtasdt0(xm,xn) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_61]),c_0_63])]),c_0_168]) ).
cnf(c_0_173,hypothesis,
xm = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_169]),c_0_170]) ).
cnf(c_0_174,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_171]),c_0_37]),c_0_38])]) ).
cnf(c_0_175,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(rw,[status(thm)],[c_0_172,c_0_115]) ).
cnf(c_0_176,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_173]),c_0_174]),c_0_175]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:41:30 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.27/1.58 % Version: 3.5.1
% 8.27/1.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.27/1.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.27/1.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.27/1.58 % Starting new_bool_3 with 300s (1) cores
% 8.27/1.58 % Starting new_bool_1 with 300s (1) cores
% 8.27/1.58 % Starting sh5l with 300s (1) cores
% 8.27/1.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2011995 completed with status 0
% 8.27/1.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.27/1.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.27/1.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.27/1.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.27/1.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.27/1.58 % No SInE strategy applied
% 8.27/1.58 % Search class: FGHSF-FFMM21-SFFFFFNN
% 8.27/1.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.27/1.58 % Starting SubtermCWHack with 136s (1) cores
% 8.27/1.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.27/1.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 8.27/1.58 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 8.27/1.58 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 8.27/1.58 % G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 2012005 completed with status 0
% 8.27/1.58 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 8.27/1.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.27/1.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.27/1.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.27/1.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.27/1.58 % No SInE strategy applied
% 8.27/1.58 % Search class: FGHSF-FFMM21-SFFFFFNN
% 8.27/1.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.27/1.58 % Starting SubtermCWHack with 136s (1) cores
% 8.27/1.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.27/1.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 8.27/1.58 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 8.27/1.58 % Preprocessing time : 0.004 s
% 8.27/1.58 % Presaturation interreduction done
% 8.27/1.58
% 8.27/1.58 % Proof found!
% 8.27/1.58 % SZS status Theorem
% 8.27/1.58 % SZS output start CNFRefutation
% See solution above
% 8.27/1.58 % Parsed axioms : 51
% 8.27/1.58 % Removed by relevancy pruning/SinE : 0
% 8.27/1.58 % Initial clauses : 94
% 8.27/1.58 % Removed in clause preprocessing : 3
% 8.27/1.58 % Initial clauses in saturation : 91
% 8.27/1.58 % Processed clauses : 4574
% 8.27/1.58 % ...of these trivial : 79
% 8.27/1.58 % ...subsumed : 3126
% 8.27/1.58 % ...remaining for further processing : 1369
% 8.27/1.58 % Other redundant clauses eliminated : 74
% 8.27/1.58 % Clauses deleted for lack of memory : 0
% 8.27/1.58 % Backward-subsumed : 221
% 8.27/1.58 % Backward-rewritten : 326
% 8.27/1.58 % Generated clauses : 24942
% 8.27/1.58 % ...of the previous two non-redundant : 23561
% 8.27/1.58 % ...aggressively subsumed : 0
% 8.27/1.58 % Contextual simplify-reflections : 235
% 8.27/1.58 % Paramodulations : 24746
% 8.27/1.58 % Factorizations : 4
% 8.27/1.58 % NegExts : 0
% 8.27/1.58 % Equation resolutions : 189
% 8.27/1.58 % Disequality decompositions : 0
% 8.27/1.58 % Total rewrite steps : 20554
% 8.27/1.58 % ...of those cached : 20444
% 8.27/1.58 % Propositional unsat checks : 0
% 8.27/1.58 % Propositional check models : 0
% 8.27/1.58 % Propositional check unsatisfiable : 0
% 8.27/1.58 % Propositional clauses : 0
% 8.27/1.58 % Propositional clauses after purity: 0
% 8.27/1.58 % Propositional unsat core size : 0
% 8.27/1.58 % Propositional preprocessing time : 0.000
% 8.27/1.58 % Propositional encoding time : 0.000
% 8.27/1.58 % Propositional solver time : 0.000
% 8.27/1.58 % Success case prop preproc time : 0.000
% 8.27/1.58 % Success case prop encoding time : 0.000
% 8.27/1.58 % Success case prop solver time : 0.000
% 8.27/1.58 % Current number of processed clauses : 734
% 8.27/1.58 % Positive orientable unit clauses : 95
% 8.27/1.58 % Positive unorientable unit clauses: 0
% 8.27/1.58 % Negative unit clauses : 38
% 8.27/1.58 % Non-unit-clauses : 601
% 8.27/1.58 % Current number of unprocessed clauses: 18797
% 8.27/1.58 % ...number of literals in the above : 104548
% 8.27/1.58 % Current number of archived formulas : 0
% 8.27/1.58 % Current number of archived clauses : 634
% 8.27/1.58 % Clause-clause subsumption calls (NU) : 109642
% 8.27/1.58 % Rec. Clause-clause subsumption calls : 41687
% 8.27/1.58 % Non-unit clause-clause subsumptions : 2074
% 8.27/1.58 % Unit Clause-clause subsumption calls : 5107
% 8.27/1.58 % Rewrite failures with RHS unbound : 0
% 8.27/1.58 % BW rewrite match attempts : 35
% 8.27/1.58 % BW rewrite match successes : 34
% 8.27/1.58 % Condensation attempts : 0
% 8.27/1.58 % Condensation successes : 0
% 8.27/1.58 % Termbank termtop insertions : 437467
% 8.27/1.58 % Search garbage collected termcells : 1370
% 8.27/1.58
% 8.27/1.58 % -------------------------------------------------
% 8.27/1.58 % User time : 1.044 s
% 8.27/1.58 % System time : 0.037 s
% 8.27/1.58 % Total time : 1.081 s
% 8.27/1.58 % Maximum resident set size: 3944 pages
% 8.27/1.58
% 8.27/1.58 % -------------------------------------------------
% 8.27/1.58 % User time : 5.215 s
% 8.27/1.58 % System time : 0.176 s
% 8.27/1.58 % Total time : 5.391 s
% 8.27/1.58 % Maximum resident set size: 4864 pages
% 8.27/1.58 % E exiting
%------------------------------------------------------------------------------