TSTP Solution File: NUM488+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM488+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:38:00 EDT 2023
% Result : Theorem 109.12s 109.48s
% Output : CNFRefutation 109.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 54
% Syntax : Number of formulae : 263 ( 88 unt; 26 typ; 0 def)
% Number of atoms : 741 ( 259 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 848 ( 344 ~; 375 |; 90 &)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 265 ( 0 sgn; 100 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aNaturalNumber0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_26,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_29,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_30,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_31,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(decl_32,type,
isPrime0: $i > $o ).
tff(decl_33,type,
xn: $i ).
tff(decl_34,type,
xm: $i ).
tff(decl_35,type,
xp: $i ).
tff(decl_36,type,
xr: $i ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1883,hypothesis,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xn
& xr = sdtmndt0(xn,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1894,hypothesis,
( xr != xn
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xn )
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xr,xm) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xr,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_28,hypothesis,
! [X96,X97] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X97)
| xp != sdtasdt0(X96,X97)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& ( ~ doDivides0(X96,xp)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_29,plain,
! [X86] :
( ( aNaturalNumber0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( doDivides0(esk4_1(X86),X86)
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( isPrime0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
cnf(c_0_30,hypothesis,
( X1 = sz10
| X1 = xp
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_33,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,hypothesis,
( esk4_1(xp) = xp
| esk4_1(xp) = sz10
| ~ aNaturalNumber0(esk4_1(xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_36,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_37,plain,
! [X83,X84] :
( ( X83 != sz00
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( X83 != sz10
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( ~ aNaturalNumber0(X84)
| ~ doDivides0(X84,X83)
| X84 = sz10
| X84 = X83
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( aNaturalNumber0(esk3_1(X83))
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( doDivides0(esk3_1(X83),X83)
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != sz10
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != X83
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_38,hypothesis,
( esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_41,plain,
! [X62,X63,X65] :
( ( aNaturalNumber0(esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( ~ aNaturalNumber0(X65)
| X63 != sdtasdt0(X62,X65)
| doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) ) ),
inference(distribute,[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_42,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,hypothesis,
( esk4_1(xp) = sz10
| doDivides0(xp,xp) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_44,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_39]),c_0_40])]) ).
fof(c_0_45,plain,
! [X29,X30,X31] :
( ( sdtasdt0(X29,X30) != sdtasdt0(X29,X31)
| X30 = X31
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31)
| X29 = sz00
| ~ aNaturalNumber0(X29) )
& ( sdtasdt0(X30,X29) != sdtasdt0(X31,X29)
| X30 = X31
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31)
| X29 = sz00
| ~ aNaturalNumber0(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_46,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,hypothesis,
doDivides0(xp,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_32])]),c_0_33]),c_0_34]),c_0_44]) ).
cnf(c_0_48,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xp,esk2_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_32])]) ).
cnf(c_0_51,hypothesis,
aNaturalNumber0(esk2_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_32])]) ).
fof(c_0_52,plain,
! [X21] :
( ( sdtasdt0(X21,sz10) = X21
| ~ aNaturalNumber0(X21) )
& ( X21 = sdtasdt0(sz10,X21)
| ~ aNaturalNumber0(X21) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_53,hypothesis,
( X1 = esk2_2(xp,xp)
| sdtasdt0(xp,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_32])]),c_0_33]) ).
cnf(c_0_54,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_55,plain,
! [X26,X27,X28] :
( ( sdtpldt0(X26,X27) != sdtpldt0(X26,X28)
| X27 = X28
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28) )
& ( sdtpldt0(X27,X26) != sdtpldt0(X28,X26)
| X27 = X28
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
fof(c_0_56,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| aNaturalNumber0(sdtasdt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_57,plain,
! [X16,X17] :
( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_58,hypothesis,
esk2_2(xp,xp) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40]),c_0_32])]) ).
cnf(c_0_59,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_61,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1883]) ).
fof(c_0_62,plain,
! [X10,X11] :
( ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X11)
| sdtpldt0(X10,X11) = sdtpldt0(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_63,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_64,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(rw,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_67,hypothesis,
( X1 = xp
| sdtpldt0(X1,xr) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_32]),c_0_61])]) ).
cnf(c_0_68,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_69,hypothesis,
( xr != xn
& aNaturalNumber0(esk11_0)
& sdtpldt0(xr,esk11_0) = xn
& sdtlseqdt0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1894])]) ).
fof(c_0_70,plain,
! [X72,X73,X74] :
( ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X74)
| ~ doDivides0(X72,X73)
| ~ doDivides0(X72,X74)
| doDivides0(X72,sdtpldt0(X73,X74)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_71,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]) ).
cnf(c_0_72,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_40]),c_0_32])]) ).
cnf(c_0_73,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_74,hypothesis,
( X1 = xp
| sdtpldt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_61])]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(xr,esk11_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,hypothesis,
aNaturalNumber0(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_78,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_40]),c_0_32])]) ).
cnf(c_0_79,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_73]),c_0_40])]) ).
cnf(c_0_80,hypothesis,
esk11_0 = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
fof(c_0_81,plain,
! [X18,X19,X20] :
( ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X20)
| sdtasdt0(sdtasdt0(X18,X19),X20) = sdtasdt0(X18,sdtasdt0(X19,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_82,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_32]),c_0_40])]),c_0_79]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[c_0_75,c_0_80]) ).
fof(c_0_84,plain,
! [X22] :
( ( sdtasdt0(X22,sz00) = sz00
| ~ aNaturalNumber0(X22) )
& ( sz00 = sdtasdt0(sz00,X22)
| ~ aNaturalNumber0(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_85,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_87,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_88,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_89,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_61])]) ).
cnf(c_0_90,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,hypothesis,
( sdtasdt0(sdtasdt0(xp,esk9_0),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_92,hypothesis,
aNaturalNumber0(sdtasdt0(xp,esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_93,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_94,plain,
! [X23,X24,X25] :
( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25) )
& ( sdtasdt0(sdtpldt0(X24,X25),X23) = sdtpldt0(sdtasdt0(X24,X23),sdtasdt0(X25,X23))
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_89]),c_0_40]),c_0_88])]) ).
cnf(c_0_96,hypothesis,
aNaturalNumber0(esk2_2(sz10,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_89]),c_0_88]),c_0_40])]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(xn,sdtasdt0(xm,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93])]) ).
cnf(c_0_98,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_99,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_100,hypothesis,
esk2_2(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_95]),c_0_96])]) ).
cnf(c_0_101,plain,
( sdtasdt0(X1,sdtasdt0(sz00,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_90]),c_0_93])]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(xn,sdtasdt0(sz00,xm)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_65]),c_0_93]),c_0_87])]) ).
cnf(c_0_103,hypothesis,
( X1 = xr
| sdtpldt0(xp,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_60]),c_0_61]),c_0_32])]) ).
cnf(c_0_104,hypothesis,
( sdtasdt0(sz10,sdtpldt0(X1,xp)) = sdtpldt0(sdtasdt0(sz10,X1),xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_72]),c_0_32]),c_0_40])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_95,c_0_100]) ).
fof(c_0_106,plain,
! [X75,X76,X77] :
( ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X75,X76)
| ~ doDivides0(X75,sdtpldt0(X76,X77))
| doDivides0(X75,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_107,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_54]),c_0_40])]) ).
cnf(c_0_108,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_65]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_87]),c_0_88])]) ).
fof(c_0_110,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = sz00
| sdtlseqdt0(X59,sdtasdt0(X59,X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_111,hypothesis,
( X1 = xr
| sdtpldt0(X1,xp) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_68]),c_0_32])]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(sdtasdt0(sz10,xr),xp) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_83]),c_0_105]),c_0_61])]) ).
cnf(c_0_113,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
fof(c_0_114,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aNaturalNumber0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aNaturalNumber0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_115,plain,
( doDivides0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_90]),c_0_93])]) ).
cnf(c_0_116,plain,
( doDivides0(X1,sdtpldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_107]) ).
cnf(c_0_117,hypothesis,
doDivides0(xm,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_87]),c_0_93])]) ).
cnf(c_0_118,hypothesis,
( doDivides0(xp,sdtpldt0(X1,xp))
| ~ doDivides0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_47]),c_0_32])]) ).
cnf(c_0_119,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_120,hypothesis,
( sdtasdt0(sz10,xr) = xr
| ~ aNaturalNumber0(sdtasdt0(sz10,xr)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_121,hypothesis,
( doDivides0(xp,X1)
| ~ doDivides0(xp,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_47]),c_0_32])]) ).
cnf(c_0_122,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_123,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_115]),c_0_93])]) ).
cnf(c_0_124,hypothesis,
doDivides0(xm,sdtpldt0(sz00,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_87]),c_0_93])]) ).
cnf(c_0_125,hypothesis,
( doDivides0(xp,sdtpldt0(sdtasdt0(xp,X1),xp))
| ~ aNaturalNumber0(sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_71]),c_0_32])]) ).
fof(c_0_126,plain,
! [X66,X67,X68] :
( ( aNaturalNumber0(X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( X67 = sdtasdt0(X66,X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( ~ aNaturalNumber0(X68)
| X67 != sdtasdt0(X66,X68)
| X68 = sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_127,plain,
! [X36,X37,X39] :
( ( aNaturalNumber0(esk1_2(X36,X37))
| ~ sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) )
& ( sdtpldt0(X36,esk1_2(X36,X37)) = X37
| ~ sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) )
& ( ~ aNaturalNumber0(X39)
| sdtpldt0(X36,X39) != X37
| sdtlseqdt0(X36,X37)
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X37) ) ),
inference(distribute,[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_128,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_65]) ).
cnf(c_0_129,hypothesis,
sdtasdt0(sz10,xr) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_64]),c_0_61]),c_0_40])]) ).
cnf(c_0_130,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_131,plain,
! [X34,X35] :
( ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35)
| sdtasdt0(X34,X35) != sz00
| X34 = sz00
| X35 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_132,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_47]),c_0_93]),c_0_32])]) ).
cnf(c_0_133,hypothesis,
doDivides0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_87])]) ).
cnf(c_0_134,hypothesis,
( doDivides0(xp,X1)
| ~ doDivides0(xp,sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_68]),c_0_32])]) ).
cnf(c_0_135,hypothesis,
( doDivides0(xp,sdtpldt0(sdtasdt0(xp,X1),xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_64]),c_0_32])]) ).
cnf(c_0_136,hypothesis,
( sdtasdt0(xp,sdtasdt0(sz10,X1)) = sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_66]),c_0_40]),c_0_32])]) ).
cnf(c_0_137,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_138,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_139,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_140,hypothesis,
sdtlseqdt0(xr,xr),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_61]),c_0_40])]),c_0_130]) ).
cnf(c_0_141,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_142,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_143,hypothesis,
sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_132]),c_0_32]),c_0_93])]) ).
cnf(c_0_144,hypothesis,
aNaturalNumber0(esk2_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_132]),c_0_93]),c_0_32])]) ).
cnf(c_0_145,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_73]),c_0_40])]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(xm,esk2_2(xm,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_133]),c_0_87])]) ).
cnf(c_0_147,hypothesis,
aNaturalNumber0(esk2_2(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_133]),c_0_87])]) ).
cnf(c_0_148,hypothesis,
( doDivides0(xp,sdtasdt0(xp,X1))
| ~ aNaturalNumber0(sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_149,hypothesis,
( aNaturalNumber0(sdtasdt0(xp,X1))
| ~ aNaturalNumber0(sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_136]),c_0_32])]) ).
cnf(c_0_150,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_137]) ).
cnf(c_0_151,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_138]) ).
cnf(c_0_152,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_122]),c_0_93])]) ).
cnf(c_0_153,hypothesis,
sdtpldt0(xr,esk1_2(xr,xr)) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_61])]) ).
cnf(c_0_154,hypothesis,
aNaturalNumber0(esk1_2(xr,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_140]),c_0_61])]) ).
cnf(c_0_155,hypothesis,
esk2_2(xp,sz00) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]),c_0_32])]),c_0_33]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_87])]) ).
cnf(c_0_157,hypothesis,
( doDivides0(xp,sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_64]),c_0_32])]) ).
cnf(c_0_158,hypothesis,
( aNaturalNumber0(sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_73]) ).
fof(c_0_159,plain,
! [X80,X81,X82] :
( ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X81)
| X80 = sz00
| ~ doDivides0(X80,X81)
| ~ aNaturalNumber0(X82)
| sdtasdt0(X82,sdtsldt0(X81,X80)) = sdtsldt0(sdtasdt0(X82,X81),X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivAsso])])]) ).
cnf(c_0_160,hypothesis,
( X1 = sz10
| sdtasdt0(xp,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_53,c_0_58]) ).
cnf(c_0_161,hypothesis,
sdtasdt0(xp,sdtsldt0(xp,xp)) = xp,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_47]),c_0_32])]),c_0_33]) ).
cnf(c_0_162,hypothesis,
aNaturalNumber0(sdtsldt0(xp,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_47]),c_0_32])]),c_0_33]) ).
cnf(c_0_163,hypothesis,
esk1_2(xr,xr) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_61])]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[c_0_143,c_0_155]) ).
cnf(c_0_165,hypothesis,
sdtlseqdt0(xm,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_156]),c_0_87]),c_0_40])]),c_0_130]) ).
cnf(c_0_166,hypothesis,
( doDivides0(xp,sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_65]),c_0_32])]) ).
cnf(c_0_167,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_65]),c_0_32])]) ).
cnf(c_0_168,plain,
( X1 = sz00
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_169,hypothesis,
sdtsldt0(xp,xp) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162])]) ).
cnf(c_0_170,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_171,hypothesis,
sdtpldt0(xr,sz00) = xr,
inference(rw,[status(thm)],[c_0_153,c_0_163]) ).
cnf(c_0_172,hypothesis,
( sdtasdt0(xp,sdtasdt0(X1,sz10)) = sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_65]),c_0_40])]) ).
cnf(c_0_173,hypothesis,
( sdtasdt0(xp,sdtasdt0(sz00,X1)) = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_164]),c_0_93]),c_0_32])]) ).
cnf(c_0_174,hypothesis,
sdtpldt0(xm,esk1_2(xm,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_165]),c_0_87])]) ).
cnf(c_0_175,hypothesis,
aNaturalNumber0(esk1_2(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_165]),c_0_87])]) ).
cnf(c_0_176,hypothesis,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(X1,xp),xp)) = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_166]),c_0_32])]),c_0_33]),c_0_167]) ).
cnf(c_0_177,hypothesis,
( sdtsldt0(sdtasdt0(X1,xp),xp) = sdtasdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_47]),c_0_169]),c_0_32])]),c_0_33]) ).
cnf(c_0_178,plain,
( sdtasdt0(sdtpldt0(X1,X2),sz10) = sdtpldt0(sdtasdt0(X1,sz10),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_54]),c_0_40])]) ).
cnf(c_0_179,hypothesis,
sdtpldt0(sz00,xr) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_171]),c_0_93]),c_0_61])]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_164]),c_0_93]),c_0_40])]) ).
cnf(c_0_181,hypothesis,
esk1_2(xm,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_174]),c_0_175]),c_0_87])]) ).
cnf(c_0_182,hypothesis,
( sdtasdt0(xp,sdtasdt0(X1,sz10)) = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_183,hypothesis,
sdtasdt0(xr,sz10) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_180]),c_0_179]),c_0_61]),c_0_93])]) ).
cnf(c_0_184,hypothesis,
sdtpldt0(xm,sz00) = xm,
inference(rw,[status(thm)],[c_0_174,c_0_181]) ).
cnf(c_0_185,hypothesis,
( doDivides0(xp,sdtasdt0(X1,sdtasdt0(X2,xp)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_85]),c_0_32])]),c_0_64]) ).
cnf(c_0_186,hypothesis,
sdtasdt0(xr,xp) = sdtasdt0(xp,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_61])]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_184]),c_0_93]),c_0_87])]) ).
cnf(c_0_188,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_85]),c_0_64]) ).
cnf(c_0_189,hypothesis,
( doDivides0(xp,sdtasdt0(X1,sdtasdt0(xp,xr)))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_61])]) ).
cnf(c_0_190,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_64]) ).
cnf(c_0_191,hypothesis,
sdtasdt0(xm,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_187]),c_0_180]),c_0_187]),c_0_87]),c_0_93])]) ).
cnf(c_0_192,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(xp,xr)))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_186]),c_0_32]),c_0_61])]) ).
fof(c_0_193,plain,
! [X69,X70,X71] :
( ~ aNaturalNumber0(X69)
| ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| ~ doDivides0(X69,X70)
| ~ doDivides0(X70,X71)
| doDivides0(X69,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_194,hypothesis,
( doDivides0(xp,sdtasdt0(xr,sdtasdt0(X1,xp)))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_61]),c_0_32])]) ).
cnf(c_0_195,hypothesis,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_191]),c_0_87])]) ).
cnf(c_0_196,hypothesis,
( aNaturalNumber0(sdtasdt0(xr,sdtasdt0(X1,xp)))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_190]),c_0_61]),c_0_32])]) ).
cnf(c_0_197,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_198,hypothesis,
doDivides0(xp,sdtasdt0(xr,sdtasdt0(xp,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_87])]) ).
cnf(c_0_199,hypothesis,
aNaturalNumber0(sdtasdt0(xr,sdtasdt0(xp,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_195]),c_0_87])]) ).
cnf(c_0_200,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_201,plain,
( doDivides0(X1,sdtasdt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_71]),c_0_64]) ).
cnf(c_0_202,hypothesis,
doDivides0(xr,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_129]),c_0_61]),c_0_40])]) ).
cnf(c_0_203,hypothesis,
( sdtasdt0(sz10,sdtasdt0(xm,X1)) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_156]),c_0_87]),c_0_40])]) ).
cnf(c_0_204,hypothesis,
aNaturalNumber0(sdtsldt0(sdtasdt0(xr,sdtasdt0(xp,xm)),xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_198]),c_0_32]),c_0_199])]),c_0_33]) ).
cnf(c_0_205,plain,
( sdtsldt0(sdtasdt0(X1,sdtasdt0(X2,X3)),X2) = sdtasdt0(X1,sdtsldt0(sdtasdt0(X2,X3),X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_71]),c_0_64]) ).
cnf(c_0_206,hypothesis,
sdtsldt0(sdtasdt0(xp,xm),xp) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_195]),c_0_191]),c_0_87])]) ).
cnf(c_0_207,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_200]),c_0_64]),c_0_71]) ).
cnf(c_0_208,hypothesis,
( doDivides0(xr,sdtasdt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_61])]) ).
cnf(c_0_209,hypothesis,
( sdtasdt0(xm,X1) = sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_203]),c_0_156]),c_0_87]),c_0_40])]) ).
cnf(c_0_210,hypothesis,
aNaturalNumber0(sdtasdt0(xr,xm)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]),c_0_61]),c_0_32]),c_0_87])]),c_0_33]) ).
cnf(c_0_211,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_79]),c_0_40])]),c_0_130]) ).
cnf(c_0_212,plain,
( sdtsldt0(X1,X1) = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_54]),c_0_40])]) ).
cnf(c_0_213,hypothesis,
doDivides0(xr,sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_87]),c_0_61])]) ).
cnf(c_0_214,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_65]),c_0_87]),c_0_61])]) ).
cnf(c_0_215,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_40])]),c_0_130]) ).
cnf(c_0_216,hypothesis,
sdtasdt0(xr,esk2_2(xr,sdtasdt0(xm,xr))) = sdtasdt0(xm,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_213]),c_0_61]),c_0_214])]) ).
cnf(c_0_217,hypothesis,
aNaturalNumber0(esk2_2(xr,sdtasdt0(xm,xr))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_213]),c_0_214]),c_0_61])]) ).
cnf(c_0_218,plain,
( sdtsldt0(sdtasdt0(X1,X2),sz10) = sdtasdt0(X1,sdtsldt0(X2,sz10))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_79]),c_0_40])]),c_0_130]) ).
cnf(c_0_219,plain,
sdtsldt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_215]),c_0_40])]),c_0_130]) ).
cnf(c_0_220,hypothesis,
sdtasdt0(sz10,sdtasdt0(xm,xr)) = sdtasdt0(xm,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_216]),c_0_217]),c_0_61])]) ).
cnf(c_0_221,plain,
( sdtsldt0(X1,sz10) = sdtasdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_54]),c_0_219]),c_0_40])]) ).
cnf(c_0_222,hypothesis,
sdtsldt0(sdtasdt0(xm,xr),sz10) = sdtasdt0(xm,xr),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_220]),c_0_40]),c_0_214])]),c_0_130]) ).
fof(c_0_223,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xr,xm) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_224,hypothesis,
( sdtasdt0(X1,xp) = sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_172,c_0_182]) ).
cnf(c_0_225,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_65]) ).
cnf(c_0_226,hypothesis,
sdtasdt0(sdtasdt0(xm,xr),sz10) = sdtasdt0(xm,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_214])]) ).
fof(c_0_227,negated_conjecture,
! [X101] :
( ( ~ aNaturalNumber0(X101)
| sdtasdt0(xr,xm) != sdtasdt0(xp,X101) )
& ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])])]) ).
cnf(c_0_228,hypothesis,
( sdtpldt0(sdtasdt0(X1,xp),sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(xp,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_224]),c_0_32])]) ).
cnf(c_0_229,hypothesis,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_191]),c_0_40]),c_0_87]),c_0_61])]) ).
cnf(c_0_230,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_231,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_232,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(sdtasdt0(X1,X3),X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_71]),c_0_64]) ).
cnf(c_0_233,hypothesis,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xm,xr)) = sdtasdt0(xp,esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_195]),c_0_60]),c_0_86]),c_0_87]),c_0_61])]) ).
cnf(c_0_234,hypothesis,
doDivides0(xp,sdtasdt0(xp,esk9_0)),
inference(rw,[status(thm)],[c_0_230,c_0_86]) ).
cnf(c_0_235,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_65]),c_0_61]),c_0_87])]) ).
cnf(c_0_236,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_234]),c_0_214]),c_0_32]),c_0_87])]),c_0_235]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM488+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 14:14:32 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 109.12/109.48 % Version : CSE_E---1.5
% 109.12/109.48 % Problem : theBenchmark.p
% 109.12/109.48 % Proof found
% 109.12/109.48 % SZS status Theorem for theBenchmark.p
% 109.12/109.48 % SZS output start Proof
% See solution above
% 109.21/109.49 % Total time : 108.586000 s
% 109.21/109.49 % SZS output end Proof
% 109.21/109.49 % Total time : 108.594000 s
%------------------------------------------------------------------------------