%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM526+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 01:55:22 PM UTC 2026
% Result : Theorem 8.86s 1.70s
% Output : CNFRefutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 147 ( 54 unt; 0 def)
% Number of atoms : 527 ( 183 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 620 ( 240 ~; 252 |; 88 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 160 ( 0 sgn 82 !; 1 ?)
% 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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(m__,conjecture,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
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/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
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/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_22,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_23,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
fof(c_0_24,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_25,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])]) ).
fof(c_0_26,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_30,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_25]) ).
fof(c_0_31,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_34,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_38,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_39,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_32]) ).
fof(c_0_44,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_45,plain,
! [X57,X58] :
( sdtlseqdt0(X58,sdtasdt0(X58,X57))
| X57 = sz00
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_46,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
fof(c_0_47,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]) ).
fof(c_0_48,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_49,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_50,plain,
! [X70,X71,X72] :
( doDivides0(X70,X72)
| ~ doDivides0(X71,X72)
| ~ doDivides0(X70,X71)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xp,xq) = xn,
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_37,c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
fof(c_0_54,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_55,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_40])]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_59,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_25]) ).
fof(c_0_60,plain,
! [X81,X82,X83] :
( sdtasdt0(X83,sdtsldt0(X82,X81)) = sdtsldt0(sdtasdt0(X83,X82),X81)
| ~ aNaturalNumber0(X83)
| ~ doDivides0(X81,X82)
| X81 = sz00
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X81) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
fof(c_0_61,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]) ).
fof(c_0_62,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])]) ).
fof(c_0_63,plain,
! [X48,X49] :
( ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| sdtlseqdt0(X49,X48) )
& ( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| sdtlseqdt0(X48,X49)
| X49 != X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
cnf(c_0_64,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,hypothesis,
doDivides0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_40])]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_68,plain,
! [X45,X46,X47] :
( sdtlseqdt0(X45,X47)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_70,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_28]),c_0_53])]) ).
cnf(c_0_71,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_40])]) ).
cnf(c_0_72,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_73,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_59]),c_0_28]),c_0_35]) ).
cnf(c_0_74,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_60]) ).
fof(c_0_75,plain,
! [X53,X54,X55] :
( ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X54,X53),sdtasdt0(X55,X53)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X54,X53) != sdtasdt0(X55,X53) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtlseqdt0(sdtasdt0(X53,X54),sdtasdt0(X53,X55)) )
& ( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X53)
| ~ sdtlseqdt0(X54,X55)
| X54 = X55
| X53 = sz00
| sdtasdt0(X53,X54) != sdtasdt0(X53,X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
cnf(c_0_76,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_78,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xq)
| doDivides0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_41]),c_0_53])]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_66]),c_0_67])]) ).
cnf(c_0_80,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_81,hypothesis,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_58]),c_0_70]),c_0_40])]),c_0_42]) ).
cnf(c_0_82,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_28]),c_0_72])]) ).
cnf(c_0_83,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_58]),c_0_40])]),c_0_42]),c_0_70])]) ).
cnf(c_0_84,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtsldt0(sdtasdt0(X1,xn),xp) = sdtasdt0(X1,xq) ),
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_74,c_0_38]),c_0_39]),c_0_41]),c_0_40])]),c_0_42]) ).
cnf(c_0_85,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_75]) ).
cnf(c_0_86,negated_conjecture,
( sdtlseqdt0(xn,xm)
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_41]),c_0_72])]) ).
cnf(c_0_87,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_88,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_67]),c_0_53])]) ).
cnf(c_0_89,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_90,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_91,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xm,xm))
| sdtlseqdt0(X1,sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_70])]) ).
cnf(c_0_92,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_41])]) ).
cnf(c_0_93,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xm))
| X1 = sz00
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_72]),c_0_41])]) ).
cnf(c_0_94,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_67]),c_0_41])]) ).
cnf(c_0_96,hypothesis,
aNaturalNumber0(esk2_2(sz10,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_88]),c_0_41]),c_0_67])]) ).
cnf(c_0_97,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xq))
| sdtlseqdt0(X1,sdtasdt0(xn,xn)) ),
inference(rw,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,hypothesis,
( sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xq))
| xm = xn ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_92]),c_0_72])]),c_0_94]) ).
cnf(c_0_100,hypothesis,
esk2_2(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_95]),c_0_96])]) ).
cnf(c_0_101,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_52]),c_0_53]),c_0_40])]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(xq,esk2_2(xq,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_53]),c_0_41])]) ).
cnf(c_0_103,hypothesis,
aNaturalNumber0(esk2_2(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_65]),c_0_41]),c_0_53])]) ).
fof(c_0_104,plain,
! [X43,X44] :
( X43 = X44
| ~ sdtlseqdt0(X44,X43)
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_105,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| xm = xn ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_95,c_0_100]) ).
cnf(c_0_107,hypothesis,
sdtasdt0(xn,esk2_2(xq,xn)) = sdtasdt0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_108,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_109,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,hypothesis,
( sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_28]),c_0_41]),c_0_72])]) ).
cnf(c_0_111,hypothesis,
doDivides0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_106]),c_0_41]),c_0_67])]) ).
cnf(c_0_112,hypothesis,
esk2_2(xq,xn) = sdtsldt0(sdtasdt0(xp,xn),xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_107]),c_0_41]),c_0_103])]),c_0_108]) ).
cnf(c_0_113,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_82])]) ).
cnf(c_0_114,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_75]) ).
cnf(c_0_115,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_97,c_0_66]),c_0_67])]) ).
cnf(c_0_116,hypothesis,
sdtasdt0(xn,esk2_2(xn,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_111]),c_0_41])]) ).
cnf(c_0_117,hypothesis,
aNaturalNumber0(esk2_2(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_111]),c_0_41])]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(xn,sdtsldt0(sdtasdt0(xp,xn),xn)) = sdtasdt0(xp,xn),
inference(rw,[status(thm)],[c_0_107,c_0_112]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X2 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_36]) ).
cnf(c_0_120,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_28]),c_0_41]),c_0_72])]) ).
cnf(c_0_121,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| sdtlseqdt0(X3,X2)
| sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
| X2 = X3
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_114,c_0_77]) ).
cnf(c_0_122,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X2) = sz00
| sdtsldt0(sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(X1,X2)) = X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_97]),c_0_28]) ).
cnf(c_0_123,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_58]),c_0_70]),c_0_40])]) ).
cnf(c_0_124,hypothesis,
esk2_2(xn,xn) = sdtsldt0(xn,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_116]),c_0_41]),c_0_117])]),c_0_108]) ).
cnf(c_0_125,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_126,hypothesis,
sdtasdt0(xp,xn) = sdtasdt0(xn,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_41]),c_0_40])]),c_0_108]) ).
cnf(c_0_127,hypothesis,
( xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
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_120,c_0_121]),c_0_72]),c_0_41])]),c_0_108]),c_0_76]) ).
cnf(c_0_128,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xn) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_106]),c_0_106]),c_0_41]),c_0_67])]),c_0_108]) ).
cnf(c_0_129,hypothesis,
sdtsldt0(sdtasdt0(xm,xm),xn) = xq,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_46]),c_0_52]),c_0_52]),c_0_53]),c_0_40])]),c_0_108]) ).
cnf(c_0_130,hypothesis,
sdtasdt0(xn,sdtsldt0(xn,xn)) = xn,
inference(rw,[status(thm)],[c_0_116,c_0_124]) ).
cnf(c_0_131,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(X1,X1) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_125]),c_0_67])]) ).
fof(c_0_132,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_133,hypothesis,
sdtsldt0(sdtasdt0(xn,xp),xn) = xp,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_126]),c_0_41]),c_0_40])]),c_0_108]) ).
cnf(c_0_134,hypothesis,
sdtsldt0(sdtasdt0(xn,xq),xm) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_92]),c_0_72])]),c_0_94]) ).
cnf(c_0_135,hypothesis,
xm = xn,
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_119,c_0_127]),c_0_128]),c_0_41]),c_0_72])]),c_0_108]) ).
cnf(c_0_136,hypothesis,
sdtsldt0(sdtasdt0(xn,xq),xn) = xq,
inference(rw,[status(thm)],[c_0_129,c_0_92]) ).
cnf(c_0_137,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_41])]),c_0_108]) ).
fof(c_0_138,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])])])])]) ).
cnf(c_0_139,hypothesis,
esk2_2(xq,xn) = xp,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_126]),c_0_133]) ).
cnf(c_0_140,hypothesis,
xq = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_135]) ).
cnf(c_0_141,hypothesis,
sdtsldt0(xn,xn) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_137]),c_0_41]),c_0_67])]),c_0_108]) ).
cnf(c_0_142,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_143,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_144,hypothesis,
xp = sz10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_124]),c_0_141]) ).
cnf(c_0_145,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_142]),c_0_67])]) ).
cnf(c_0_146,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_145]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM526+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:38:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 8.86/1.70 % Version: 3.5.1
% 8.86/1.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.70 % Starting new_bool_3 with 300s (1) cores
% 8.86/1.70 % Starting new_bool_1 with 300s (1) cores
% 8.86/1.70 % Starting sh5l with 300s (1) cores
% 8.86/1.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4056090 completed with status 0
% 8.86/1.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.86/1.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.86/1.70 % No SInE strategy applied
% 8.86/1.70 % Search class: FGHSF-FFMM21-SFFFFFNN
% 8.86/1.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.86/1.70 % Starting SubtermCWHack with 136s (1) cores
% 8.86/1.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.86/1.70 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 8.86/1.70 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 8.86/1.70 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 8.86/1.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4056107 completed with status 0
% 8.86/1.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.86/1.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.86/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.86/1.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.86/1.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.86/1.70 % No SInE strategy applied
% 8.86/1.70 % Search class: FGHSF-FFMM21-SFFFFFNN
% 8.86/1.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.86/1.70 % Starting SubtermCWHack with 136s (1) cores
% 8.86/1.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.86/1.70 % Preprocessing time : 0.002 s
% 8.86/1.70 % Presaturation interreduction done
% 8.86/1.70
% 8.86/1.70 % Proof found!
% 8.86/1.70 % SZS status Theorem
% 8.86/1.70 % SZS output start CNFRefutation
% See solution above
% 8.86/1.70 % Parsed axioms : 47
% 8.86/1.70 % Removed by relevancy pruning/SinE : 0
% 8.86/1.70 % Initial clauses : 85
% 8.86/1.70 % Removed in clause preprocessing : 3
% 8.86/1.70 % Initial clauses in saturation : 82
% 8.86/1.70 % Processed clauses : 7712
% 8.86/1.70 % ...of these trivial : 476
% 8.86/1.70 % ...subsumed : 4521
% 8.86/1.70 % ...remaining for further processing : 2715
% 8.86/1.70 % Other redundant clauses eliminated : 208
% 8.86/1.70 % Clauses deleted for lack of memory : 0
% 8.86/1.70 % Backward-subsumed : 270
% 8.86/1.70 % Backward-rewritten : 1345
% 8.86/1.70 % Generated clauses : 58534
% 8.86/1.70 % ...of the previous two non-redundant : 51287
% 8.86/1.70 % ...aggressively subsumed : 0
% 8.86/1.70 % Contextual simplify-reflections : 275
% 8.86/1.70 % Paramodulations : 58285
% 8.86/1.70 % Factorizations : 8
% 8.86/1.70 % NegExts : 0
% 8.86/1.70 % Equation resolutions : 223
% 8.86/1.70 % Disequality decompositions : 0
% 8.86/1.70 % Total rewrite steps : 79086
% 8.86/1.70 % ...of those cached : 78374
% 8.86/1.70 % Propositional unsat checks : 0
% 8.86/1.70 % Propositional check models : 0
% 8.86/1.70 % Propositional check unsatisfiable : 0
% 8.86/1.70 % Propositional clauses : 0
% 8.86/1.70 % Propositional clauses after purity: 0
% 8.86/1.70 % Propositional unsat core size : 0
% 8.86/1.70 % Propositional preprocessing time : 0.000
% 8.86/1.70 % Propositional encoding time : 0.000
% 8.86/1.70 % Propositional solver time : 0.000
% 8.86/1.70 % Success case prop preproc time : 0.000
% 8.86/1.70 % Success case prop encoding time : 0.000
% 8.86/1.70 % Success case prop solver time : 0.000
% 8.86/1.70 % Current number of processed clauses : 994
% 8.86/1.70 % Positive orientable unit clauses : 384
% 8.86/1.70 % Positive unorientable unit clauses: 0
% 8.86/1.70 % Negative unit clauses : 94
% 8.86/1.70 % Non-unit-clauses : 516
% 8.86/1.70 % Current number of unprocessed clauses: 42636
% 8.86/1.70 % ...number of literals in the above : 187004
% 8.86/1.70 % Current number of archived formulas : 0
% 8.86/1.70 % Current number of archived clauses : 1710
% 8.86/1.70 % Clause-clause subsumption calls (NU) : 157473
% 8.86/1.70 % Rec. Clause-clause subsumption calls : 75751
% 8.86/1.70 % Non-unit clause-clause subsumptions : 3228
% 8.86/1.70 % Unit Clause-clause subsumption calls : 27454
% 8.86/1.70 % Rewrite failures with RHS unbound : 0
% 8.86/1.70 % BW rewrite match attempts : 351
% 8.86/1.70 % BW rewrite match successes : 195
% 8.86/1.70 % Condensation attempts : 0
% 8.86/1.70 % Condensation successes : 0
% 8.86/1.70 % Termbank termtop insertions : 1134698
% 8.86/1.70 % Search garbage collected termcells : 1409
% 8.86/1.70
% 8.86/1.70 % -------------------------------------------------
% 8.86/1.70 % User time : 1.174 s
% 8.86/1.70 % System time : 0.050 s
% 8.86/1.70 % Total time : 1.225 s
% 8.86/1.70 % Maximum resident set size: 3940 pages
% 8.86/1.70
% 8.86/1.70 % -------------------------------------------------
% 8.86/1.70 % User time : 4.729 s
% 8.86/1.70 % System time : 0.179 s
% 8.86/1.70 % Total time : 4.908 s
% 8.86/1.70 % Maximum resident set size: 4608 pages
% 8.86/1.70 % E exiting
%------------------------------------------------------------------------------