TSTP Solution File: NUM510+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM510+1 : 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 : n025.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 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 52
% Syntax : Number of formulae : 182 ( 47 unt; 20 typ; 0 def)
% Number of atoms : 586 ( 192 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 706 ( 282 ~; 307 |; 75 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 189 ( 0 sgn; 98 !; 2 ?; 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 ).
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(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(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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(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(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(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
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(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(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(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(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(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__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_32,plain,
! [X60,X61,X63] :
( ( aNaturalNumber0(esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( ~ aNaturalNumber0(X63)
| X61 != sdtasdt0(X60,X63)
| doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) ) ),
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_33,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_34,plain,
! [X64,X65,X66] :
( ( aNaturalNumber0(X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( X65 = sdtasdt0(X64,X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( ~ aNaturalNumber0(X66)
| X65 != sdtasdt0(X64,X66)
| X66 = sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_35,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X19] :
( ( sdtasdt0(X19,sz10) = X19
| ~ aNaturalNumber0(X19) )
& ( X19 = sdtasdt0(sz10,X19)
| ~ aNaturalNumber0(X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_38,plain,
! [X49,X50,X51] :
( ( sdtpldt0(X51,X49) != sdtpldt0(X51,X50)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X51,X49),sdtpldt0(X51,X50))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtpldt0(X49,X51) != sdtpldt0(X50,X51)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X49,X51),sdtpldt0(X50,X51))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_39,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_34]) ).
cnf(c_0_40,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_47,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_48,plain,
! [X13] :
( ( sdtpldt0(X13,sz00) = X13
| ~ aNaturalNumber0(X13) )
& ( X13 = sdtpldt0(sz00,X13)
| ~ aNaturalNumber0(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_49,plain,
! [X67,X68,X69] :
( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X67,X68)
| ~ doDivides0(X68,X69)
| doDivides0(X67,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_50,plain,
! [X32,X33] :
( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X33)
| sdtasdt0(X32,X33) != sz00
| X32 = sz00
| X33 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_51,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_53,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_54,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_55,plain,
! [X44,X45,X46] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X46)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X46)
| sdtlseqdt0(X44,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_56,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xn),sdtpldt0(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_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_57,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_59,plain,
! [X34,X35,X37] :
( ( aNaturalNumber0(esk1_2(X34,X35))
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( ~ aNaturalNumber0(X37)
| sdtpldt0(X34,X37) != X35
| sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_60,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| aNaturalNumber0(sdtpldt0(X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_61,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_64,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,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_51,c_0_52]),c_0_42])]),c_0_53]) ).
cnf(c_0_66,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xn),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_45])]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_46]),c_0_63])]) ).
fof(c_0_72,plain,
! [X56,X57] :
( ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| X56 = sz00
| sdtlseqdt0(X57,sdtasdt0(X57,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_73,plain,
! [X14,X15] :
( ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15)
| sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_74,plain,
( sdtsldt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_42])]),c_0_53])]),c_0_58])]) ).
cnf(c_0_75,plain,
( aNaturalNumber0(sdtsldt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_42])]),c_0_53]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45])]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_70]) ).
cnf(c_0_78,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_52]),c_0_42]),c_0_63])]) ).
fof(c_0_79,negated_conjecture,
~ ( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_80,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_58])]) ).
cnf(c_0_83,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_57]),c_0_46])]) ).
cnf(c_0_84,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_57]),c_0_58])]) ).
cnf(c_0_85,hypothesis,
sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn,
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_78]),c_0_42]),c_0_46])]),c_0_53]) ).
cnf(c_0_86,hypothesis,
aNaturalNumber0(sdtsldt0(xn,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_42]),c_0_46])]),c_0_53]) ).
fof(c_0_87,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,hypothesis,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_62]),c_0_63]),c_0_46])]) ).
cnf(c_0_90,hypothesis,
( xr = sz00
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_62]),c_0_63]),c_0_46])]) ).
cnf(c_0_91,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_34]) ).
fof(c_0_92,plain,
! [X70,X71,X72] :
( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72)
| ~ doDivides0(X70,X71)
| ~ doDivides0(X70,X72)
| doDivides0(X70,sdtpldt0(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_93,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_82]),c_0_58])]) ).
cnf(c_0_94,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_95,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_58]),c_0_46])]) ).
cnf(c_0_96,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_97,plain,
! [X27,X28,X29] :
( ( sdtasdt0(X27,X28) != sdtasdt0(X27,X29)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) )
& ( sdtasdt0(X28,X27) != sdtasdt0(X29,X27)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_98,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_85]),c_0_86])]) ).
cnf(c_0_99,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_100,hypothesis,
( xr = sz00
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63])]),c_0_90]) ).
cnf(c_0_101,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_91]),c_0_36]),c_0_40]) ).
cnf(c_0_102,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_92]) ).
cnf(c_0_103,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_93]),c_0_42]),c_0_58])]) ).
fof(c_0_104,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_45]),c_0_58])]) ).
cnf(c_0_106,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_45]),c_0_58])]) ).
cnf(c_0_107,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_85,c_0_98]) ).
cnf(c_0_109,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
fof(c_0_110,plain,
! [X81,X82] :
( ( X81 != sz00
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( X81 != sz10
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( ~ aNaturalNumber0(X82)
| ~ doDivides0(X82,X81)
| X82 = sz10
| X82 = X81
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( aNaturalNumber0(esk3_1(X81))
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( doDivides0(esk3_1(X81),X81)
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != sz10
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != X81
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) ) ),
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_111,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_101,c_0_41]),c_0_42])]),c_0_53]) ).
cnf(c_0_112,plain,
( sdtsldt0(X1,sz10) = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_65]),c_0_42])]),c_0_75]) ).
cnf(c_0_113,plain,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_58]),c_0_42])]),c_0_52]) ).
cnf(c_0_114,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_115,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_105]),c_0_106])]) ).
cnf(c_0_116,hypothesis,
( xn = sz00
| 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_107,c_0_108]),c_0_46]),c_0_42])]) ).
cnf(c_0_117,hypothesis,
( sdtasdt0(xr,xn) = xn
| xr = sz00 ),
inference(spm,[status(thm)],[c_0_89,c_0_109]) ).
cnf(c_0_118,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
fof(c_0_119,plain,
! [X24,X25,X26] :
( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) )
& ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_120,plain,
( sz00 = X1
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
fof(c_0_121,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X76,X77)
| X77 = sz00
| sdtlseqdt0(X76,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_122,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_58])]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_105,c_0_115]) ).
cnf(c_0_124,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_125,hypothesis,
( xr = sz00
| xr = sz10
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_63])]) ).
cnf(c_0_126,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_118]),c_0_42])]) ).
cnf(c_0_127,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_129,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sdtpldt0(sz00,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_120]),c_0_42])]) ).
cnf(c_0_130,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_131,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_45])]) ).
cnf(c_0_132,hypothesis,
( xn = sz00
| xr = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_133,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_58])]) ).
cnf(c_0_134,hypothesis,
( xp = X1
| sdtpldt0(sz00,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_123]),c_0_45]),c_0_58])]) ).
cnf(c_0_135,hypothesis,
( sdtpldt0(sz00,xn) = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_70]),c_0_46]),c_0_58])]) ).
cnf(c_0_136,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_45]),c_0_42])]) ).
cnf(c_0_137,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_138,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_132]),c_0_133]) ).
fof(c_0_139,plain,
! [X20] :
( ( sdtasdt0(X20,sz00) = sz00
| ~ aNaturalNumber0(X20) )
& ( sz00 = sdtasdt0(sz00,X20)
| ~ aNaturalNumber0(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_140,plain,
! [X30,X31] :
( ( X30 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( X31 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(sz10,xp),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_46])]),c_0_47]),c_0_136]) ).
cnf(c_0_142,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_143,hypothesis,
doDivides0(xp,sdtasdt0(sz00,xm)),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_144,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_145,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_146,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_147,hypothesis,
sdtpldt0(sz10,esk1_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_141]),c_0_45]),c_0_42])]) ).
cnf(c_0_148,hypothesis,
aNaturalNumber0(esk1_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_141]),c_0_45]),c_0_42])]) ).
fof(c_0_149,plain,
! [X42,X43] :
( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X43)
| ~ sdtlseqdt0(X42,X43)
| ~ sdtlseqdt0(X43,X42)
| X42 = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_150,hypothesis,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(spm,[status(thm)],[c_0_142,c_0_138]) ).
cnf(c_0_151,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145])]) ).
cnf(c_0_152,hypothesis,
xp != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_42])]),c_0_53]) ).
cnf(c_0_153,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_154,hypothesis,
sdtsldt0(sz00,xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_144]),c_0_145])]) ).
cnf(c_0_155,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_66,c_0_151]),c_0_45]),c_0_58])]),c_0_152]) ).
fof(c_0_156,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_157,plain,
( sdtasdt0(X1,X2) = X1
| X2 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_80]),c_0_36]) ).
cnf(c_0_158,hypothesis,
sdtasdt0(xp,xk) = sz00,
inference(rw,[status(thm)],[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_151]),c_0_45]),c_0_58])]),c_0_152]),c_0_154]) ).
cnf(c_0_159,hypothesis,
aNaturalNumber0(xk),
inference(rw,[status(thm)],[c_0_155,c_0_154]) ).
cnf(c_0_160,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_161,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_95]),c_0_45]),c_0_159])]),c_0_152]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 10:41:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.71 % Version : CSE_E---1.5
% 0.19/0.71 % Problem : theBenchmark.p
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark.p
% 0.19/0.71 % SZS output start Proof
% See solution above
% 0.19/0.73 % Total time : 0.137000 s
% 0.19/0.73 % SZS output end Proof
% 0.19/0.73 % Total time : 0.141000 s
%------------------------------------------------------------------------------