%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM502+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:20 PM UTC 2026
% Result : Theorem 240.84s 35.86s
% Output : CNFRefutation 240.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 31
% Syntax : Number of formulae : 210 ( 27 unt; 0 def)
% Number of atoms : 824 ( 334 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 1008 ( 394 ~; 454 |; 104 &)
% ( 6 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 266 ( 1 sgn 118 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
( sdtlseqdt0(xk,xp)
& xk != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(c_0_31,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_32,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_33,plain,
! [X79,X80,X81] :
( ( ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79)
| ~ doDivides0(X79,X80)
| X79 = sz00
| X81 = sdtsldt0(X80,X79)
| X80 != sdtasdt0(X79,X81)
| ~ aNaturalNumber0(X81) )
& ( ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79)
| ~ doDivides0(X79,X80)
| X79 = sz00
| X81 != sdtsldt0(X80,X79)
| X80 = sdtasdt0(X79,X81) )
& ( ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79)
| ~ doDivides0(X79,X80)
| X79 = sz00
| X81 != sdtsldt0(X80,X79)
| aNaturalNumber0(X81) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])]) ).
fof(c_0_34,plain,
! [X61,X62,X63] :
( ( ~ aNaturalNumber0(X61)
| X61 = sz00
| ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X62)
| X62 = X63
| sdtasdt0(X62,X61) != sdtasdt0(X63,X61) )
& ( ~ aNaturalNumber0(X61)
| X61 = sz00
| ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X62)
| X62 = X63
| sdtasdt0(X61,X62) != sdtasdt0(X61,X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_36]) ).
fof(c_0_40,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| sdtasdt0(X3,sdtsldt0(X1,X2)) != X1
| X3 = X2
| X2 = sz00
| sdtsldt0(X1,X2) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_43,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_45,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_46,plain,
! [X53,X54] :
( aNaturalNumber0(sdtasdt0(X53,X54))
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_47,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(X1,xk) != sdtasdt0(xn,xm)
| X1 = xp
| xp = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]),c_0_45]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_50,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_52,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_53,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xk) != sdtasdt0(xn,xm)
| X1 = xp
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_54,hypothesis,
( xp = sz00
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_49]),c_0_50])]) ).
fof(c_0_55,plain,
! [X55,X56] :
( sdtasdt0(X55,X56) = sdtasdt0(X56,X55)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_56,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_57,plain,
! [X73] :
( ( ~ aNaturalNumber0(X73)
| X73 = sdtasdt0(sz10,X73) )
& ( ~ aNaturalNumber0(X73)
| sdtasdt0(X73,sz10) = X73 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_58,plain,
! [X57,X58,X59] :
( sdtasdt0(sdtasdt0(X57,X58),X59) = sdtasdt0(X57,sdtasdt0(X58,X59))
| ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_59,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_52]) ).
cnf(c_0_60,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xk) != sdtasdt0(xp,xk)
| X1 = xp
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,hypothesis,
( aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_66,plain,
! [X66,X67,X69] :
( ( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X66)
| doDivides0(X66,X67)
| X67 != sdtasdt0(X66,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X66)
| ~ doDivides0(X66,X67)
| X67 = sdtasdt0(X66,esk2_2(X66,X67)) )
& ( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X66)
| ~ doDivides0(X66,X67)
| aNaturalNumber0(esk2_2(X66,X67)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
cnf(c_0_67,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xk,X1) != sdtasdt0(xp,xk)
| X1 = xp
| xp = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_68,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]),c_0_48]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_71,plain,
! [X60] :
( ( ~ aNaturalNumber0(X60)
| sz00 = sdtasdt0(sz00,X60) )
& ( ~ aNaturalNumber0(X60)
| sdtasdt0(X60,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_72,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,sz10))
| sdtasdt0(xk,X1) != sdtasdt0(xp,xk)
| xp = sz00
| sdtasdt0(X1,sz10) = xp ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_48]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_70]),c_0_65])]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_79,plain,
! [X38,X39,X40] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ aNaturalNumber0(X38)
| sdtasdt0(sdtpldt0(X39,X40),X38) = sdtpldt0(sdtasdt0(X39,X38),sdtasdt0(X40,X38)) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ aNaturalNumber0(X38)
| sdtasdt0(X38,sdtpldt0(X39,X40)) = sdtpldt0(sdtasdt0(X38,X39),sdtasdt0(X38,X40)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_80,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xk,X1) != sdtasdt0(xp,xk)
| xp = sz00
| sdtasdt0(X1,sz10) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_48]),c_0_65])]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(esk2_2(X1,sdtasdt0(X1,X2)))
| X1 = sz00
| esk2_2(X1,sdtasdt0(X1,X2)) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74])]),c_0_48]),c_0_75]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_83,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_86,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xk) != sdtasdt0(xp,xk)
| xp = sz00
| sdtasdt0(X1,sz10) = xp ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_61]),c_0_62]) ).
cnf(c_0_87,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_88,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDivAsso]) ).
cnf(c_0_89,plain,
( ~ aNaturalNumber0(esk2_2(sz10,sz00))
| esk2_2(sz10,sz00) = sz00 ),
inference(condense,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_78]),c_0_65])]),c_0_83])]) ).
cnf(c_0_90,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_91,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(X1,sdtpldt0(X2,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_78])]) ).
cnf(c_0_92,hypothesis,
( xp = sz00
| sdtasdt0(xp,sz10) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_44])]) ).
fof(c_0_93,plain,
! [X37] :
( ( ~ aNaturalNumber0(X37)
| X37 = sdtpldt0(sz00,X37) )
& ( ~ aNaturalNumber0(X37)
| sdtpldt0(X37,sz00) = X37 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_94,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_87]),c_0_48]),c_0_75]) ).
fof(c_0_95,plain,
! [X82,X83,X84] :
( sdtasdt0(X84,sdtsldt0(X83,X82)) = sdtsldt0(sdtasdt0(X84,X83),X82)
| ~ aNaturalNumber0(X84)
| ~ doDivides0(X82,X83)
| X82 = sz00
| ~ aNaturalNumber0(X83)
| ~ aNaturalNumber0(X82) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])])]) ).
cnf(c_0_96,plain,
( ~ doDivides0(sz10,sz00)
| esk2_2(sz10,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_78]),c_0_65])]) ).
fof(c_0_97,plain,
! [X44,X45] :
( ( ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X44)
| sdtpldt0(X44,X45) != sz00
| X45 = sz00 )
& ( ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X44)
| sdtpldt0(X44,X45) != sz00
| X44 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
fof(c_0_98,plain,
! [X34,X35,X36] :
( sdtpldt0(sdtpldt0(X34,X35),X36) = sdtpldt0(X34,sdtpldt0(X35,X36))
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ aNaturalNumber0(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
fof(c_0_99,plain,
! [X30,X31] :
( aNaturalNumber0(sdtpldt0(X30,X31))
| ~ aNaturalNumber0(X31)
| ~ aNaturalNumber0(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_100,plain,
! [X32,X33] :
( sdtpldt0(X32,X33) = sdtpldt0(X33,X32)
| ~ aNaturalNumber0(X33)
| ~ aNaturalNumber0(X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_101,hypothesis,
( xp = sz00
| sdtasdt0(xp,sdtpldt0(sz10,sz00)) = sdtpldt0(xp,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_65]),c_0_44])]) ).
cnf(c_0_102,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,plain,
( ~ aNaturalNumber0(X1)
| sdtsldt0(X1,sz10) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_70]),c_0_65])]),c_0_83]) ).
cnf(c_0_104,plain,
( ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_105,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_70]),c_0_65])]) ).
cnf(c_0_106,plain,
( ~ doDivides0(sz10,sz00)
| sdtasdt0(sz10,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_96]),c_0_65]),c_0_78])]) ).
cnf(c_0_107,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_85]),c_0_78])]) ).
cnf(c_0_108,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_110,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_111,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_112,hypothesis,
( xp = sz00
| sdtpldt0(xp,sz00) = sdtasdt0(xp,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_65])]) ).
cnf(c_0_113,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtsldt0(X2,sz10)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_65])]),c_0_83]),c_0_48]),c_0_105]) ).
cnf(c_0_114,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_77]),c_0_78])]) ).
cnf(c_0_115,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_65])]) ).
cnf(c_0_116,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,sdtpldt0(X3,X1)) != sz00
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_117,hypothesis,
( xp = sz00
| sdtpldt0(sz00,xp) = sdtasdt0(xp,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_78]),c_0_44])]) ).
cnf(c_0_118,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtsldt0(X1,sz10))
| sdtsldt0(X1,sz10) = sdtasdt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_113]),c_0_65])]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(X1,X1) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_63]),c_0_65])]) ).
cnf(c_0_120,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_121,hypothesis,
( xp = sz00
| sdtasdt0(sz00,xp) = sdtasdt0(sz00,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_92]),c_0_65]),c_0_44])]) ).
cnf(c_0_122,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_115]),c_0_78]),c_0_65])]) ).
fof(c_0_123,negated_conjecture,
~ ( sdtlseqdt0(xk,xp)
& xk != xp ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_124,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sdtasdt0(xp,sz10)) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_44]),c_0_78])]) ).
cnf(c_0_125,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_65])]),c_0_83]) ).
cnf(c_0_126,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_70]),c_0_65])]) ).
cnf(c_0_127,hypothesis,
( xp = sz00
| sdtasdt0(sz00,xp) = sz00 ),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
fof(c_0_128,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_129,negated_conjecture,
~ ( sdtlseqdt0(xk,xp)
& xk != xp ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
cnf(c_0_130,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sdtasdt0(sz10,xp)) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_61]),c_0_65]),c_0_44])]) ).
cnf(c_0_131,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_70]),c_0_65])]) ).
fof(c_0_132,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_133,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,sz10)
| X2 = sz00
| sdtasdt0(X1,sdtsldt0(sz10,X2)) = sdtsldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_63]),c_0_65])]) ).
cnf(c_0_134,plain,
doDivides0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_125]),c_0_65])]) ).
cnf(c_0_135,hypothesis,
( xp = sz00
| sdtasdt0(sdtpldt0(sz00,sz10),xp) = sdtpldt0(sz00,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_44]),c_0_78])]) ).
cnf(c_0_136,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_137,plain,
! [X11,X12,X13] :
( sdtlseqdt0(X11,X13)
| ~ sdtlseqdt0(X12,X13)
| ~ sdtlseqdt0(X11,X12)
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
fof(c_0_138,plain,
! [X14,X15] :
( ( ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X14)
| sdtlseqdt0(X14,X15)
| sdtlseqdt0(X15,X14) )
& ( ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X14)
| sdtlseqdt0(X14,X15)
| X15 != X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])])]) ).
fof(c_0_139,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])]) ).
cnf(c_0_140,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtpldt0(X1,xp)) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_44])]) ).
fof(c_0_141,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X4)
| sdtlseqdt0(X4,X5)
| sdtpldt0(X4,X7) != X5
| ~ aNaturalNumber0(X7) )
& ( ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X4,X5)
| sdtpldt0(X4,esk1_2(X4,X5)) = X5 )
& ( ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X4,X5)
| aNaturalNumber0(esk1_2(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])]) ).
fof(c_0_142,plain,
! [X23,X24] :
( sdtlseqdt0(X24,sdtasdt0(X24,X23))
| X23 = sz00
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])]) ).
fof(c_0_143,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
cnf(c_0_144,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,X1)
| X2 = sz00
| sdtasdt0(sz10,sdtsldt0(X1,X2)) = sdtsldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_70]),c_0_65])]) ).
cnf(c_0_145,hypothesis,
( xp = sz00
| sdtsldt0(sdtasdt0(xp,xk),xp) = xk ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_146,hypothesis,
( aNaturalNumber0(sdtasdt0(xp,xk))
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_49]),c_0_50])]) ).
cnf(c_0_147,hypothesis,
( doDivides0(xp,sdtasdt0(xp,xk))
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_148,plain,
( ~ aNaturalNumber0(X1)
| sdtsldt0(X1,sz10) = sdtasdt0(X1,sz10) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_133]),c_0_65]),c_0_134])]),c_0_83]) ).
cnf(c_0_149,hypothesis,
( xp = sz00
| sdtpldt0(sz00,xp) = sdtasdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_65])]) ).
cnf(c_0_150,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_151,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_152,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_153,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtpldt0(xp,X1)) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_111]),c_0_44])]) ).
cnf(c_0_154,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_155,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
fof(c_0_156,plain,
! [X9,X10] :
( X9 = X10
| ~ sdtlseqdt0(X10,X9)
| ~ sdtlseqdt0(X9,X10)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_157,plain,
! [X19,X20,X21] :
( ( ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19)
| ~ sdtlseqdt0(X20,X21)
| X20 = X21
| X19 = sz00
| sdtlseqdt0(sdtasdt0(X20,X19),sdtasdt0(X21,X19)) )
& ( ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19)
| ~ sdtlseqdt0(X20,X21)
| X20 = X21
| X19 = sz00
| sdtasdt0(X20,X19) != sdtasdt0(X21,X19) )
& ( ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19)
| ~ sdtlseqdt0(X20,X21)
| X20 = X21
| X19 = sz00
| sdtlseqdt0(sdtasdt0(X19,X20),sdtasdt0(X19,X21)) )
& ( ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19)
| ~ sdtlseqdt0(X20,X21)
| X20 = X21
| X19 = sz00
| sdtasdt0(X19,X20) != sdtasdt0(X19,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])]) ).
fof(c_0_158,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
cnf(c_0_159,hypothesis,
( xp = sz00
| sdtasdt0(sz10,xk) = xk ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_44])]),c_0_146]),c_0_147]) ).
cnf(c_0_160,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtasdt0(X1,sz10)) = X1 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_148]),c_0_65])]),c_0_83]),c_0_105]) ).
cnf(c_0_161,hypothesis,
( xp = sz00
| sdtasdt0(xp,sz10) = sdtasdt0(sz10,xp) ),
inference(spm,[status(thm)],[c_0_117,c_0_149]) ).
cnf(c_0_162,hypothesis,
( aNaturalNumber0(sdtasdt0(xp,sz10))
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_112]),c_0_78]),c_0_44])]) ).
cnf(c_0_163,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X3,X2)
| sdtlseqdt0(X3,X1)
| sdtlseqdt0(X1,X2) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_164,negated_conjecture,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xp,xk)
| xk = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_151]),c_0_44])]) ).
cnf(c_0_165,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(esk1_2(xp,X1))
| ~ sdtlseqdt0(xp,X1)
| sdtasdt0(sz10,X1) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_44])]) ).
cnf(c_0_166,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_167,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| sdtlseqdt0(X2,X1)
| X2 = sz00
| sdtsldt0(X1,X2) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_38]),c_0_39]) ).
cnf(c_0_168,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_169,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| X1 = X3
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_170,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
fof(c_0_171,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
inference(fof_nnf,[status(thm)],[c_0_158]) ).
cnf(c_0_172,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_155,c_0_61]) ).
cnf(c_0_173,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,X1) != xk
| xk = X1
| xp = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_159]),c_0_65])]),c_0_83]),c_0_62]) ).
cnf(c_0_174,hypothesis,
( xp = sz00
| sdtasdt0(sz10,sdtasdt0(sz10,xp)) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_44])]) ).
cnf(c_0_175,hypothesis,
( aNaturalNumber0(sdtasdt0(sz10,xp))
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_61]),c_0_65]),c_0_44])]) ).
cnf(c_0_176,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X1,xk)
| sdtlseqdt0(xp,X1)
| xk = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_44])]) ).
fof(c_0_177,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
cnf(c_0_178,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X1)
| sdtasdt0(sz10,X1) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_44])]) ).
cnf(c_0_179,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| xp = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_167]),c_0_43]),c_0_44])]),c_0_45]) ).
cnf(c_0_180,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sdtasdt0(X3,X1),sdtasdt0(X2,X1))
| X2 = X3
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_48]),c_0_48]),c_0_37]) ).
cnf(c_0_181,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xm,X1)
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,X1))
| xm = X1
| xn = sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_54]),c_0_49]),c_0_50])]) ).
cnf(c_0_182,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_183,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_184,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X3,X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X3))
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_172]),c_0_48]) ).
cnf(c_0_185,hypothesis,
( xk != xp
| xp = sz00
| sdtasdt0(sz10,xp) = xk ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
cnf(c_0_186,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xk)
| xk = xp
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_176,c_0_62]) ).
fof(c_0_187,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_nnf,[status(thm)],[c_0_177]) ).
cnf(c_0_188,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(sz10,sdtasdt0(xn,xm)) != sz00
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_189,hypothesis,
( ~ sdtlseqdt0(xm,xk)
| xp = sz00
| xn = sz00
| xm = xk ),
inference(csr,[status(thm)],[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_180,c_0_181]),c_0_182]),c_0_44]),c_0_50])]),c_0_45]),c_0_183]),c_0_62]) ).
cnf(c_0_190,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xk)
| sdtlseqdt0(xp,X1)
| xp = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_44]),c_0_65])]),c_0_83]),c_0_186]) ).
cnf(c_0_191,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_192,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) != sz00
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_188,c_0_70]) ).
cnf(c_0_193,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_194,hypothesis,
( xm = xk
| xn = sz00
| xp = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_49])]),c_0_191]) ).
cnf(c_0_195,hypothesis,
( xp = sz00
| sdtasdt0(sz00,sdtasdt0(xp,xk)) = sdtasdt0(sz00,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_54]),c_0_49]),c_0_50])]) ).
cnf(c_0_196,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_197,hypothesis,
( sdtasdt0(xn,xm) != sz00
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_198,hypothesis,
( xk != xp
| xp = sz00
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_199,hypothesis,
( xp = sz00
| sdtasdt0(sz00,xm) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_195]),c_0_146]) ).
fof(c_0_200,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
cnf(c_0_201,hypothesis,
( sdtlseqdt0(xk,xp)
| xp = sz00
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_196,c_0_194]) ).
cnf(c_0_202,hypothesis,
( xk != xp
| xp = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_199]) ).
fof(c_0_203,plain,
! [X74,X75] :
( ( ~ aNaturalNumber0(X74)
| isPrime0(X74)
| X74 = sz10
| X74 = sz00
| esk3_1(X74) != X74 )
& ( ~ aNaturalNumber0(X74)
| isPrime0(X74)
| X74 = sz10
| X74 = sz00
| esk3_1(X74) != sz10 )
& ( ~ aNaturalNumber0(X74)
| isPrime0(X74)
| X74 = sz10
| X74 = sz00
| doDivides0(esk3_1(X74),X74) )
& ( ~ aNaturalNumber0(X74)
| isPrime0(X74)
| X74 = sz10
| X74 = sz00
| aNaturalNumber0(esk3_1(X74)) )
& ( ~ aNaturalNumber0(X74)
| ~ isPrime0(X74)
| X75 = X74
| X75 = sz10
| ~ doDivides0(X75,X74)
| ~ aNaturalNumber0(X75) )
& ( ~ aNaturalNumber0(X74)
| ~ isPrime0(X74)
| X74 != sz10 )
& ( ~ aNaturalNumber0(X74)
| ~ isPrime0(X74)
| X74 != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])])])])])]) ).
cnf(c_0_204,negated_conjecture,
( xn = sz00
| xp = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_201]),c_0_202]) ).
cnf(c_0_205,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_206,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_207,hypothesis,
xp = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_204]),c_0_199]) ).
cnf(c_0_208,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_205]),c_0_78])]) ).
cnf(c_0_209,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207]),c_0_208]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM502+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.50 % Computer : n010.cluster.edu
% 0.09/0.50 % Model : x86_64 x86_64
% 0.09/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.50 % Memory : 8046.5625MB
% 0.09/0.50 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 02:35:40 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.54 Running first-order theorem proving
% 0.09/0.54 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 240.84/35.86 % Version: 3.5.1
% 240.84/35.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 240.84/35.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 240.84/35.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 240.84/35.86 % Starting new_bool_3 with 300s (1) cores
% 240.84/35.86 % Starting new_bool_1 with 300s (1) cores
% 240.84/35.86 % Starting sh5l with 300s (1) cores
% 240.84/35.86 % sh5l with pid 4052441 completed with status 0
% 240.84/35.86 % Result found by sh5l
% 240.84/35.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 240.84/35.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 240.84/35.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 240.84/35.86 % Starting new_bool_3 with 300s (1) cores
% 240.84/35.86 % Starting new_bool_1 with 300s (1) cores
% 240.84/35.86 % Starting sh5l with 300s (1) cores
% 240.84/35.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 240.84/35.86 % SinE strategy is gf500_gu_R04_F100_L20000
% 240.84/35.86 % Search class: FGHSF-FFMM21-SFFFFFNN
% 240.84/35.86 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 240.84/35.86 % Starting SubtermCWHack with 28s (1) cores
% 240.84/35.86 % SubtermCWHack with pid 4052448 completed with status 8
% 240.84/35.86 % Starting sh5l with 31s (1) cores
% 240.84/35.86 % sh5l with pid 4052483 completed with status 0
% 240.84/35.86 % Result found by sh5l
% 240.84/35.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 240.84/35.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 240.84/35.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 240.84/35.86 % Starting new_bool_3 with 300s (1) cores
% 240.84/35.86 % Starting new_bool_1 with 300s (1) cores
% 240.84/35.86 % Starting sh5l with 300s (1) cores
% 240.84/35.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 240.84/35.86 % SinE strategy is gf500_gu_R04_F100_L20000
% 240.84/35.86 % Search class: FGHSF-FFMM21-SFFFFFNN
% 240.84/35.86 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 240.84/35.86 % Starting SubtermCWHack with 28s (1) cores
% 240.84/35.86 % SubtermCWHack with pid 4052448 completed with status 8
% 240.84/35.86 % Starting sh5l with 31s (1) cores
% 240.84/35.86 % Preprocessing time : 0.004 s
% 240.84/35.86 % Presaturation interreduction done
% 240.84/35.86
% 240.84/35.86 % Proof found!
% 240.84/35.86 % SZS status Theorem
% 240.84/35.86 % SZS output start CNFRefutation
% See solution above
% 240.84/35.86 % Parsed axioms : 50
% 240.84/35.86 % Removed by relevancy pruning/SinE : 1
% 240.84/35.86 % Initial clauses : 90
% 240.84/35.86 % Removed in clause preprocessing : 3
% 240.84/35.86 % Initial clauses in saturation : 87
% 240.84/35.86 % Processed clauses : 14230
% 240.84/35.86 % ...of these trivial : 148
% 240.84/35.86 % ...subsumed : 11566
% 240.84/35.86 % ...remaining for further processing : 2516
% 240.84/35.86 % Other redundant clauses eliminated : 362
% 240.84/35.86 % Clauses deleted for lack of memory : 0
% 240.84/35.86 % Backward-subsumed : 466
% 240.84/35.86 % Backward-rewritten : 1156
% 240.84/35.86 % Generated clauses : 130228
% 240.84/35.86 % ...of the previous two non-redundant : 121068
% 240.84/35.86 % ...aggressively subsumed : 0
% 240.84/35.86 % Contextual simplify-reflections : 954
% 240.84/35.86 % Paramodulations : 129794
% 240.84/35.86 % Factorizations : 56
% 240.84/35.86 % NegExts : 0
% 240.84/35.86 % Equation resolutions : 378
% 240.84/35.86 % Disequality decompositions : 0
% 240.84/35.86 % Total rewrite steps : 108045
% 240.84/35.86 % ...of those cached : 108008
% 240.84/35.86 % Propositional unsat checks : 0
% 240.84/35.86 % Propositional check models : 0
% 240.84/35.86 % Propositional check unsatisfiable : 0
% 240.84/35.86 % Propositional clauses : 0
% 240.84/35.86 % Propositional clauses after purity: 0
% 240.84/35.86 % Propositional unsat core size : 0
% 240.84/35.86 % Propositional preprocessing time : 0.000
% 240.84/35.86 % Propositional encoding time : 0.000
% 240.84/35.86 % Propositional solver time : 0.000
% 240.84/35.86 % Success case prop preproc time : 0.000
% 240.84/35.86 % Success case prop encoding time : 0.000
% 240.84/35.86 % Success case prop solver time : 0.000
% 240.84/35.86 % Current number of processed clauses : 806
% 240.84/35.86 % Positive orientable unit clauses : 32
% 240.84/35.86 % Positive unorientable unit clauses: 0
% 240.84/35.86 % Negative unit clauses : 13
% 240.84/35.86 % Non-unit-clauses : 761
% 240.84/35.86 % Current number of unprocessed clauses: 105894
% 240.84/35.86 % ...number of literals in the above : 828733
% 240.84/35.86 % Current number of archived formulas : 0
% 240.84/35.86 % Current number of archived clauses : 1702
% 240.84/35.86 % Clause-clause subsumption calls (NU) : 787351
% 240.84/35.86 % Rec. Clause-clause subsumption calls : 134713
% 240.84/35.86 % Non-unit clause-clause subsumptions : 11001
% 240.84/35.86 % Unit Clause-clause subsumption calls : 1450
% 240.84/35.86 % Rewrite failures with RHS unbound : 0
% 240.84/35.86 % BW rewrite match attempts : 13
% 240.84/35.86 % BW rewrite match successes : 13
% 240.84/35.86 % Condensation attempts : 14230
% 240.84/35.86 % Condensation successes : 110
% 240.84/35.86 % Termbank termtop insertions : 3062312
% 240.84/35.86 % Search garbage collected termcells : 1322
% 240.84/35.86
% 240.84/35.86 % -------------------------------------------------
% 240.84/35.86 % User time : 33.314 s
% 240.84/35.86 % System time : 1.213 s
% 240.84/35.86 % Total time : 34.526 s
% 240.84/35.86 % Maximum resident set size: 3944 pages
% 240.84/35.86
% 240.84/35.86 % -------------------------------------------------
% 240.84/35.86 % User time : 33.318 s
% 240.84/35.86 % System time : 1.219 s
% 240.84/35.86 % Total time : 34.538 s
% 240.84/35.86 % Maximum resident set size: 4608 pages
% 240.84/35.86 % E exiting
%------------------------------------------------------------------------------