TSTP Solution File: NUM510+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM510+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 : n001.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 10:38:13 EDT 2023
% Result : Theorem 0.84s 0.98s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 63
% Syntax : Number of formulae : 203 ( 55 unt; 34 typ; 0 def)
% Number of atoms : 634 ( 241 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 723 ( 258 ~; 299 |; 129 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 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 : 29 ( 29 usr; 17 con; 0-3 aty)
% Number of variables : 173 ( 0 sgn; 83 !; 13 ?; 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,
xk: $i ).
tff(decl_37,type,
xr: $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_1: $i > $i ).
tff(decl_42,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_0: $i ).
tff(decl_52,type,
esk15_0: $i ).
tff(decl_53,type,
esk16_0: $i ).
tff(decl_54,type,
esk17_0: $i ).
tff(decl_55,type,
esk18_0: $i ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
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(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(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(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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(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(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
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(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(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(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(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__2377,hypothesis,
( xk != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(m__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(m__,conjecture,
( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) = xn )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(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(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_29,hypothesis,
! [X104,X105] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X105)
| xr != sdtasdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& ( ~ doDivides0(X104,xr)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
fof(c_0_30,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_31,hypothesis,
( X1 = sz10
| X1 = xr
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
xr != sz10,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
( esk4_1(xr) = xr
| esk4_1(xr) = sz10
| ~ aNaturalNumber0(esk4_1(xr)) ),
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_32]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_37,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,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])])])])]) ).
fof(c_0_39,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])])])]) ).
cnf(c_0_40,hypothesis,
( esk4_1(xr) = sz10
| esk4_1(xr) = xr ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_41,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_43,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_39]) ).
cnf(c_0_44,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,hypothesis,
( esk4_1(xr) = sz10
| doDivides0(xr,xr) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_46,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42])]) ).
cnf(c_0_47,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_48,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_49,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_50,hypothesis,
doDivides0(xr,xr),
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_44,c_0_45]),c_0_33])]),c_0_34]),c_0_35]),c_0_46]) ).
cnf(c_0_51,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,hypothesis,
sdtasdt0(xr,sdtsldt0(xr,xr)) = xr,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_33])]),c_0_34]) ).
cnf(c_0_54,hypothesis,
aNaturalNumber0(sdtsldt0(xr,xr)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_33])]),c_0_34]) ).
fof(c_0_55,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])])]) ).
fof(c_0_56,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_57,hypothesis,
( sdtsldt0(xr,xr) = X1
| sdtasdt0(xr,X1) != xr
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_33])]),c_0_34]) ).
cnf(c_0_58,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,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_56]) ).
fof(c_0_60,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_61,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])])])])]) ).
fof(c_0_62,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_63,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_64,hypothesis,
sdtsldt0(xr,xr) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_42]),c_0_33])]) ).
fof(c_0_65,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_66,hypothesis,
( doDivides0(xr,X1)
| ~ doDivides0(xr,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_50]),c_0_33])]) ).
cnf(c_0_67,hypothesis,
sdtpldt0(xr,esk13_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_69,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_70,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,hypothesis,
sdtasdt0(xr,sz10) = xr,
inference(rw,[status(thm)],[c_0_53,c_0_64]) ).
cnf(c_0_74,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,hypothesis,
doDivides0(xr,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_76,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_71]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(sz10,xr) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_42]),c_0_33])]) ).
fof(c_0_78,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_79,hypothesis,
( doDivides0(X1,esk13_0)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_69]),c_0_33])]) ).
cnf(c_0_80,hypothesis,
doDivides0(sz10,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_42]),c_0_33])]) ).
cnf(c_0_81,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_78]) ).
cnf(c_0_82,hypothesis,
doDivides0(sz10,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_42])]) ).
cnf(c_0_83,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,esk13_0))
| ~ doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_69]),c_0_42])]) ).
cnf(c_0_84,hypothesis,
doDivides0(sz10,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_67]),c_0_33])]) ).
cnf(c_0_85,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_86,hypothesis,
( xk != xp
& aNaturalNumber0(esk15_0)
& sdtpldt0(xk,esk15_0) = xp
& sdtlseqdt0(xk,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2377])]) ).
cnf(c_0_87,hypothesis,
( doDivides0(sz10,X1)
| ~ doDivides0(sz10,sdtpldt0(xk,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_84]),c_0_85]),c_0_42])]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(xk,esk15_0) = xp,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_89,hypothesis,
aNaturalNumber0(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_90,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_91,hypothesis,
( doDivides0(sz10,esk15_0)
| ~ doDivides0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]) ).
cnf(c_0_92,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_90]),c_0_42])]) ).
cnf(c_0_93,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_94,hypothesis,
doDivides0(sz10,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]) ).
cnf(c_0_95,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,esk15_0))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_94]),c_0_89]),c_0_42])]),c_0_92]) ).
cnf(c_0_96,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_88]),c_0_85])]) ).
cnf(c_0_97,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_98,plain,
! [X78,X79] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| ~ doDivides0(X78,X79)
| X79 = sz00
| sdtlseqdt0(X78,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
fof(c_0_99,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_100,negated_conjecture,
~ ( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) = xn )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(sz10,sdtsldt0(xp,sz10)) = xp,
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_96]),c_0_42]),c_0_93])]),c_0_97]) ).
cnf(c_0_102,hypothesis,
aNaturalNumber0(sdtsldt0(xp,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_96]),c_0_42]),c_0_93])]),c_0_97]) ).
cnf(c_0_103,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,xr))
| ~ doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_33]),c_0_42])]) ).
fof(c_0_104,plain,
! [X10,X11] :
( ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X11)
| sdtpldt0(X10,X11) = sdtpldt0(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_105,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_106,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_107,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_109,negated_conjecture,
! [X112] :
( ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X112)
| sdtpldt0(sdtsldt0(xn,xr),X112) != xn
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X112)
| sdtpldt0(sdtsldt0(xn,xr),X112) != xn
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn )
& ( ~ aNaturalNumber0(X112)
| sdtpldt0(sdtsldt0(xn,xr),X112) != xn
| sdtsldt0(xn,xr) = xn )
& ( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])]) ).
cnf(c_0_110,hypothesis,
sdtsldt0(xp,sz10) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_101]),c_0_102])]) ).
cnf(c_0_111,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,xr))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_92]) ).
cnf(c_0_112,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_113,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_114,hypothesis,
( sz00 = xn
| sdtlseqdt0(xr,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_33])]) ).
cnf(c_0_115,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_116,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_117,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_118,negated_conjecture,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_119,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
fof(c_0_120,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_121,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(rw,[status(thm)],[c_0_101,c_0_110]) ).
cnf(c_0_122,hypothesis,
( doDivides0(sz10,sdtpldt0(xr,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_33])]) ).
cnf(c_0_123,hypothesis,
( sdtpldt0(xr,esk1_2(xr,xn)) = xn
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_108]),c_0_33])]) ).
cnf(c_0_124,hypothesis,
( sz00 = xn
| aNaturalNumber0(esk1_2(xr,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_114]),c_0_108]),c_0_33])]) ).
cnf(c_0_125,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_39]) ).
cnf(c_0_126,hypothesis,
( X1 = esk18_0
| sdtasdt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_116]),c_0_117]),c_0_33])]),c_0_34]) ).
cnf(c_0_127,negated_conjecture,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(cn,[status(thm)],[c_0_118]) ).
cnf(c_0_128,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cn,[status(thm)],[c_0_119]) ).
cnf(c_0_129,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_130,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_121]),c_0_93]),c_0_42])]) ).
cnf(c_0_131,hypothesis,
( sz00 = xn
| doDivides0(sz10,xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_132,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_125]),c_0_71]),c_0_76]) ).
cnf(c_0_133,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_134,negated_conjecture,
sdtsldt0(xn,xr) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]) ).
cnf(c_0_135,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_72]) ).
cnf(c_0_136,hypothesis,
doDivides0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_130]),c_0_93]),c_0_42])]) ).
fof(c_0_137,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_138,hypothesis,
( sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn
| sz00 = xn ),
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_131]),c_0_42]),c_0_108])]),c_0_97]) ).
cnf(c_0_139,plain,
( sdtsldt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_90]),c_0_42])]),c_0_97]) ).
cnf(c_0_140,negated_conjecture,
( esk18_0 = xn
| ~ sdtlseqdt0(esk18_0,xn) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_134]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_116]),c_0_117]),c_0_33])]),c_0_34]) ).
cnf(c_0_142,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_59,c_0_136]),c_0_93])]) ).
cnf(c_0_143,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_144,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_145,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])])])])]) ).
cnf(c_0_146,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_147,hypothesis,
( sdtasdt0(sz10,xn) = xn
| sz00 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_108])]) ).
cnf(c_0_148,negated_conjecture,
esk18_0 = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
fof(c_0_149,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_150,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_142,c_0_143]),c_0_136]),c_0_144]),c_0_93])]) ).
cnf(c_0_151,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_145]) ).
fof(c_0_152,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_153,hypothesis,
( sz00 = xn
| sz10 = X1
| sdtasdt0(X1,xn) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_108]),c_0_42])]) ).
cnf(c_0_154,hypothesis,
sdtasdt0(xr,xn) = xn,
inference(rw,[status(thm)],[c_0_116,c_0_148]) ).
cnf(c_0_155,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00,
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_150]),c_0_93]),c_0_144])]),c_0_151]) ).
cnf(c_0_157,hypothesis,
aNaturalNumber0(sdtsldt0(sz00,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_150]),c_0_93]),c_0_144])]),c_0_151]) ).
fof(c_0_158,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_159,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_160,hypothesis,
sz00 = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_33])]),c_0_35]) ).
cnf(c_0_161,hypothesis,
sdtsldt0(sz00,xp) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_93])]),c_0_151]) ).
cnf(c_0_162,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_163,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_164,plain,
( sdtasdt0(xn,X1) = xn
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_160]) ).
cnf(c_0_165,hypothesis,
sdtsldt0(xn,xp) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_160]),c_0_160]) ).
cnf(c_0_166,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_167,hypothesis,
xk != xn,
inference(rw,[status(thm)],[c_0_162,c_0_160]) ).
cnf(c_0_168,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]),c_0_166])]),c_0_167]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM510+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 14:44:14 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.54 start to proof: theBenchmark
% 0.84/0.98 % Version : CSE_E---1.5
% 0.84/0.98 % Problem : theBenchmark.p
% 0.84/0.98 % Proof found
% 0.84/0.98 % SZS status Theorem for theBenchmark.p
% 0.84/0.98 % SZS output start Proof
% See solution above
% 0.84/0.99 % Total time : 0.427000 s
% 0.84/0.99 % SZS output end Proof
% 0.84/0.99 % Total time : 0.430000 s
%------------------------------------------------------------------------------