%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM528+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 : n001.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 01:49:26 PM UTC 2026
% Result : Theorem 0.22s 5.72s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 115 ( 32 unt; 0 def)
% Number of atoms : 420 ( 153 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 494 ( 189 ~; 198 |; 68 &)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 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 : 123 ( 0 sgn 71 !; 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(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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
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(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
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(m__3152,hypothesis,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3152) ).
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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
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(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,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_26,plain,
! [X56,X57,X58] :
( ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ doDivides0(X56,X57)
| X56 = sz00
| X58 = sdtsldt0(X57,X56)
| X57 != sdtasdt0(X56,X58)
| ~ aNaturalNumber0(X58) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ doDivides0(X56,X57)
| X56 = sz00
| X58 != sdtsldt0(X57,X56)
| X57 = sdtasdt0(X56,X58) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ doDivides0(X56,X57)
| X56 = sz00
| X58 != sdtsldt0(X57,X56)
| aNaturalNumber0(X58) ) ),
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_27,plain,
! [X34,X35] :
( aNaturalNumber0(sdtasdt0(X34,X35))
| ~ aNaturalNumber0(X35)
| ~ aNaturalNumber0(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_28,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X19,X20] :
( sdtlseqdt0(X20,sdtasdt0(X20,X19))
| X19 = sz00
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_30,plain,
! [X36,X37] :
( sdtasdt0(X36,X37) = sdtasdt0(X37,X36)
| ~ aNaturalNumber0(X37)
| ~ aNaturalNumber0(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_31,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_32,plain,
! [X72,X73] :
( ( ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X72)
| sdtlseqdt0(X72,X73)
| sdtlseqdt0(X73,X72) )
& ( ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X72)
| sdtlseqdt0(X72,X73)
| X73 != X72 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
cnf(c_0_33,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_26]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
fof(c_0_41,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_44,plain,
! [X38,X39,X40] :
( sdtasdt0(sdtasdt0(X38,X39),X40) = sdtasdt0(X38,sdtasdt0(X39,X40))
| ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ aNaturalNumber0(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_46,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_47,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_49,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_34]) ).
fof(c_0_51,plain,
! [X67,X68] :
( X67 = X68
| ~ sdtlseqdt0(X68,X67)
| ~ sdtlseqdt0(X67,X68)
| ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_52,hypothesis,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3152])]) ).
cnf(c_0_53,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_54,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_55,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_37])]) ).
fof(c_0_56,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_57,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xm)
| sdtlseqdt0(xm,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_58,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_59,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,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_45,c_0_46]),c_0_47]),c_0_37]),c_0_48])]),c_0_49]) ).
cnf(c_0_62,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_50,c_0_46]),c_0_47]),c_0_37]),c_0_48])]),c_0_49]) ).
cnf(c_0_63,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_43])]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_36]),c_0_37])]),c_0_49]) ).
cnf(c_0_67,hypothesis,
( ~ aNaturalNumber0(xq)
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
fof(c_0_68,plain,
! [X69,X70,X71] :
( sdtlseqdt0(X69,X71)
| ~ sdtlseqdt0(X70,X71)
| ~ sdtlseqdt0(X69,X70)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_69,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_70,hypothesis,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
fof(c_0_71,plain,
! [X9,X10,X11] :
( ( ~ aNaturalNumber0(X9)
| X9 = sz00
| ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X10)
| X10 = X11
| sdtasdt0(X10,X9) != sdtasdt0(X11,X9) )
& ( ~ aNaturalNumber0(X9)
| X9 = sz00
| ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X10)
| X10 = X11
| sdtasdt0(X9,X10) != sdtasdt0(X9,X11) ) ),
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_58])])])])]) ).
fof(c_0_72,plain,
! [X90] :
( ( ~ aNaturalNumber0(X90)
| X90 = sdtasdt0(sz10,X90) )
& ( ~ aNaturalNumber0(X90)
| sdtasdt0(X90,sz10) = X90 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_73,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_59]) ).
cnf(c_0_74,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_60,c_0_61]),c_0_62]),c_0_37])]) ).
fof(c_0_75,plain,
! [X14,X15] :
( X15 = sz00
| X14 = sz00
| sdtasdt0(X14,X15) != sz00
| ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_76,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm)
| sdtasdt0(xm,xm) = sdtasdt0(xn,xn) ),
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_66]) ).
cnf(c_0_77,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_62])]) ).
cnf(c_0_78,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_79,negated_conjecture,
( sdtlseqdt0(xn,xm)
| xm = xn ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_48]) ).
fof(c_0_81,plain,
! [X41,X42,X44] :
( ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| doDivides0(X41,X42)
| X42 != sdtasdt0(X41,X44)
| ~ aNaturalNumber0(X44) )
& ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| ~ doDivides0(X41,X42)
| X42 = sdtasdt0(X41,esk3_2(X41,X42)) )
& ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| ~ doDivides0(X41,X42)
| aNaturalNumber0(esk3_2(X41,X42)) ) ),
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_82,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_84,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_74]),c_0_62])]) ).
cnf(c_0_86,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_87,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_88,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtasdt0(xm,xm) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_89,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X1,xm)
| xm = 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_43]),c_0_48])]) ).
cnf(c_0_90,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_80,c_0_48]) ).
fof(c_0_91,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_92,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_93,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != X2
| X2 = sz00
| X1 = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_94,hypothesis,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_36,c_0_85]) ).
cnf(c_0_95,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xq)),
inference(rw,[status(thm)],[c_0_77,c_0_85]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xn,xq) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_85]),c_0_43])]),c_0_87]) ).
cnf(c_0_97,negated_conjecture,
( xm = xn
| sdtasdt0(xm,xm) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_48])]) ).
fof(c_0_98,plain,
! [X22,X23] :
( ( ~ aNaturalNumber0(X22)
| isPrime0(X22)
| X22 = sz10
| X22 = sz00
| esk1_1(X22) != X22 )
& ( ~ aNaturalNumber0(X22)
| isPrime0(X22)
| X22 = sz10
| X22 = sz00
| esk1_1(X22) != sz10 )
& ( ~ aNaturalNumber0(X22)
| isPrime0(X22)
| X22 = sz10
| X22 = sz00
| doDivides0(esk1_1(X22),X22) )
& ( ~ aNaturalNumber0(X22)
| isPrime0(X22)
| X22 = sz10
| X22 = sz00
| aNaturalNumber0(esk1_1(X22)) )
& ( ~ aNaturalNumber0(X22)
| ~ isPrime0(X22)
| X23 = X22
| X23 = sz10
| ~ doDivides0(X23,X22)
| ~ aNaturalNumber0(X23) )
& ( ~ aNaturalNumber0(X22)
| ~ isPrime0(X22)
| X22 != sz10 )
& ( ~ aNaturalNumber0(X22)
| ~ isPrime0(X22)
| X22 != 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_91])])])])])]) ).
cnf(c_0_99,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_26]) ).
cnf(c_0_100,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_92]),c_0_35]) ).
cnf(c_0_101,hypothesis,
( sdtasdt0(xn,xq) != sdtasdt0(xn,xn)
| xp = sz10 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_37])]),c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( xm = xn
| sdtasdt0(xn,xq) = sdtasdt0(xn,xn) ),
inference(spm,[status(thm)],[c_0_97,c_0_85]) ).
cnf(c_0_103,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_104,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_99]),c_0_35]),c_0_100]) ).
cnf(c_0_105,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_106,negated_conjecture,
( xp = sz10
| xm = xn ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_103]),c_0_84])]) ).
cnf(c_0_108,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_104,c_0_85]),c_0_43])]),c_0_87]) ).
cnf(c_0_109,hypothesis,
xm = xn,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_110,hypothesis,
sdtsldt0(sdtasdt0(xn,xq),xn) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_109]) ).
cnf(c_0_111,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_112,hypothesis,
xq = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_110]),c_0_48]),c_0_62])]),c_0_111]) ).
cnf(c_0_113,hypothesis,
xp = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_112])]) ).
cnf(c_0_114,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_113]),c_0_107]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM528+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.45 % Computer : n001.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Mon Sep 21 02:43:33 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.51 Running first-order theorem proving
% 0.22/5.51 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
% 0.22/5.72 % Version: 3.5.1
% 0.22/5.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.72 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.72 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.72 % Starting sh5l with 300s (1) cores
% 0.22/5.72 % new_bool_3 with pid 2014834 completed with status 0
% 0.22/5.72 % Result found by new_bool_3
% 0.22/5.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.72 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.72 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.72 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.72 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.22/5.72 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.72 % Starting SubtermCWHack with 28s (1) cores
% 0.22/5.72 % SubtermCWHack with pid 2014837 completed with status 0
% 0.22/5.72 % Result found by SubtermCWHack
% 0.22/5.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.72 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.72 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.72 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.72 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.22/5.72 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.72 % Starting SubtermCWHack with 28s (1) cores
% 0.22/5.72 % Preprocessing time : 0.002 s
% 0.22/5.72
% 0.22/5.72 % Proof found!
% 0.22/5.72 % SZS status Theorem
% 0.22/5.72 % SZS output start CNFRefutation
% See solution above
% 0.22/5.72 % Parsed axioms : 48
% 0.22/5.72 % Removed by relevancy pruning/SinE : 1
% 0.22/5.72 % Initial clauses : 83
% 0.22/5.72 % Removed in clause preprocessing : 3
% 0.22/5.72 % Initial clauses in saturation : 80
% 0.22/5.72 % Processed clauses : 2121
% 0.22/5.72 % ...of these trivial : 37
% 0.22/5.72 % ...subsumed : 1250
% 0.22/5.72 % ...remaining for further processing : 834
% 0.22/5.72 % Other redundant clauses eliminated : 54
% 0.22/5.72 % Clauses deleted for lack of memory : 0
% 0.22/5.72 % Backward-subsumed : 63
% 0.22/5.72 % Backward-rewritten : 440
% 0.22/5.72 % Generated clauses : 9012
% 0.22/5.72 % ...of the previous two non-redundant : 7460
% 0.22/5.72 % ...aggressively subsumed : 0
% 0.22/5.72 % Contextual simplify-reflections : 51
% 0.22/5.72 % Paramodulations : 8948
% 0.22/5.72 % Factorizations : 1
% 0.22/5.72 % NegExts : 0
% 0.22/5.72 % Equation resolutions : 61
% 0.22/5.72 % Disequality decompositions : 0
% 0.22/5.72 % Total rewrite steps : 10553
% 0.22/5.72 % ...of those cached : 10458
% 0.22/5.72 % Propositional unsat checks : 0
% 0.22/5.72 % Propositional check models : 0
% 0.22/5.72 % Propositional check unsatisfiable : 0
% 0.22/5.72 % Propositional clauses : 0
% 0.22/5.72 % Propositional clauses after purity: 0
% 0.22/5.72 % Propositional unsat core size : 0
% 0.22/5.72 % Propositional preprocessing time : 0.000
% 0.22/5.72 % Propositional encoding time : 0.000
% 0.22/5.72 % Propositional solver time : 0.000
% 0.22/5.72 % Success case prop preproc time : 0.000
% 0.22/5.72 % Success case prop encoding time : 0.000
% 0.22/5.72 % Success case prop solver time : 0.000
% 0.22/5.72 % Current number of processed clauses : 321
% 0.22/5.72 % Positive orientable unit clauses : 55
% 0.22/5.72 % Positive unorientable unit clauses: 0
% 0.22/5.72 % Negative unit clauses : 11
% 0.22/5.72 % Non-unit-clauses : 255
% 0.22/5.72 % Current number of unprocessed clauses: 5211
% 0.22/5.72 % ...number of literals in the above : 23383
% 0.22/5.72 % Current number of archived formulas : 0
% 0.22/5.72 % Current number of archived clauses : 505
% 0.22/5.72 % Clause-clause subsumption calls (NU) : 20820
% 0.22/5.72 % Rec. Clause-clause subsumption calls : 12753
% 0.22/5.72 % Non-unit clause-clause subsumptions : 1186
% 0.22/5.72 % Unit Clause-clause subsumption calls : 1828
% 0.22/5.72 % Rewrite failures with RHS unbound : 0
% 0.22/5.72 % BW rewrite match attempts : 43
% 0.22/5.72 % BW rewrite match successes : 43
% 0.22/5.72 % Condensation attempts : 0
% 0.22/5.72 % Condensation successes : 0
% 0.22/5.72 % Termbank termtop insertions : 155120
% 0.22/5.72 % Search garbage collected termcells : 1359
% 0.22/5.72
% 0.22/5.72 % -------------------------------------------------
% 0.22/5.72 % User time : 0.162 s
% 0.22/5.72 % System time : 0.014 s
% 0.22/5.72 % Total time : 0.175 s
% 0.22/5.72 % Maximum resident set size: 3940 pages
% 0.22/5.72
% 0.22/5.72 % -------------------------------------------------
% 0.22/5.72 % User time : 0.163 s
% 0.22/5.72 % System time : 0.019 s
% 0.22/5.72 % Total time : 0.182 s
% 0.22/5.72 % Maximum resident set size: 4864 pages
% 0.22/5.72 % E exiting
%------------------------------------------------------------------------------