%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM510+3 : 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 : n019.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 01:49:22 PM UTC 2026
% Result : Theorem 0.23s 1.06s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 22 unt; 0 def)
% Number of atoms : 286 ( 137 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 318 ( 105 ~; 109 |; 79 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__2342,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(m__,conjecture,
( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ? [X1] :
( sdtpldt0(sdtsldt0(xn,xr),X1) = xn
& aNaturalNumber0(X1) ) ) )
& ~ ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2487,hypothesis,
( doDivides0(xr,xn)
& ? [X1] :
( xn = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
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__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1870,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [X1] :
( sdtpldt0(xp,X1) = xn
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(c_0_14,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_15,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
inference(fof_simplification,[status(thm)],[m__2342]) ).
fof(c_0_16,negated_conjecture,
~ ( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ? [X1] :
( sdtpldt0(sdtsldt0(xn,xr),X1) = xn
& aNaturalNumber0(X1) ) ) )
& ~ ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_17,plain,
! [X30,X31,X32] :
( ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X31,X30) != sdtasdt0(X32,X30) )
& ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X30,X31) != sdtasdt0(X30,X32) ) ),
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_14])])])])]) ).
fof(c_0_18,hypothesis,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,esk18_0)
& aNaturalNumber0(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_19,hypothesis,
! [X107,X108] :
( isPrime0(xr)
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| ~ doDivides0(X107,xr) )
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| xr != sdtasdt0(X107,X108)
| ~ aNaturalNumber0(X108) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk12_0)
& aNaturalNumber0(esk12_0)
& aNaturalNumber0(xr) ),
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_15])])])])])]) ).
fof(c_0_20,negated_conjecture,
! [X115] :
( ( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) )
& ( sdtsldt0(xn,xr) = xn
| sdtpldt0(sdtsldt0(xn,xr),X115) != xn
| ~ aNaturalNumber0(X115) )
& ( sdtsldt0(xn,xr) = xn
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),X115) != xn
| ~ aNaturalNumber0(X115) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),X115) != xn
| ~ aNaturalNumber0(X115) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
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_16])])])])]) ).
fof(c_0_21,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]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X69,X70,X71] :
( ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 = sdtsldt0(X70,X69)
| X70 != sdtasdt0(X69,X71)
| ~ aNaturalNumber0(X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| X70 = sdtasdt0(X69,X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| aNaturalNumber0(X71) ) ),
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_21])])])])]) ).
cnf(c_0_30,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xr,X1) != xn
| X1 = esk18_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(cn,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cn,[status(thm)],[c_0_28]) ).
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,plain,
! [X17,X18] :
( sdtasdt0(X17,X18) = sdtasdt0(X18,X17)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
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_29]) ).
cnf(c_0_36,negated_conjecture,
sdtsldt0(xn,xr) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_40,plain,
! [X59,X60] :
( sdtlseqdt0(X60,sdtasdt0(X60,X59))
| X59 = sz00
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( X1 != esk18_0
| sdtasdt0(xr,X1) = 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_35,c_0_36]),c_0_37]),c_0_25]),c_0_38])]),c_0_26]) ).
cnf(c_0_43,negated_conjecture,
( X1 != esk18_0
| aNaturalNumber0(X1) ),
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_39,c_0_36]),c_0_37]),c_0_25]),c_0_38])]),c_0_26]) ).
cnf(c_0_44,negated_conjecture,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( X1 != esk18_0
| sdtasdt0(X1,xr) = xn ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25])]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ sdtlseqdt0(esk18_0,xn)
| esk18_0 = xn ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_36]),c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( X1 != esk18_0
| sdtlseqdt0(X1,xn) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_25])]),c_0_26]),c_0_43]) ).
cnf(c_0_49,negated_conjecture,
esk18_0 = xn,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_50,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xr,xn) = xn,
inference(rw,[status(thm)],[c_0_23,c_0_49]) ).
fof(c_0_53,plain,
! [X22] :
( ( ~ aNaturalNumber0(X22)
| X22 = sdtasdt0(sz10,X22) )
& ( ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sz10) = X22 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_54,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_50]) ).
fof(c_0_55,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
fof(c_0_56,plain,
! [X23] :
( ( ~ aNaturalNumber0(X23)
| sz00 = sdtasdt0(sz00,X23) )
& ( ~ aNaturalNumber0(X23)
| sdtasdt0(X23,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_57,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xn) != xn
| xr = X1
| sz00 = 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_38]),c_0_25])]) ).
cnf(c_0_58,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,hypothesis,
xr != sz10,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_64,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,hypothesis,
sz00 = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_38])]),c_0_60]) ).
fof(c_0_67,hypothesis,
! [X102] :
( ~ sdtlseqdt0(xp,xn)
& ( sdtpldt0(xp,X102) != xn
| ~ aNaturalNumber0(X102) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])])]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_61]),c_0_62]),c_0_63])]),c_0_64]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xn,X1) = xn ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66]) ).
cnf(c_0_70,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_71,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM510+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.68 % Computer : n019.cluster.edu
% 0.17/0.68 % Model : x86_64 x86_64
% 0.17/0.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.68 % Memory : 8046.5625MB
% 0.17/0.68 % OS : Linux 6.8.0-71-generic
% 0.17/0.68 % CPULimit : 300
% 0.17/0.68 % WCLimit : 300
% 0.17/0.68 % DateTime : Mon Sep 21 02:36:20 UTC 2026
% 0.17/0.69 % CPUTime :
% 0.17/0.69 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.77 Running first-order theorem proving
% 0.23/0.77 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
% 0.23/1.06 % Version: 3.5.1
% 0.23/1.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/1.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/1.06 % Starting new_bool_3 with 300s (1) cores
% 0.23/1.06 % Starting new_bool_1 with 300s (1) cores
% 0.23/1.06 % Starting sh5l with 300s (1) cores
% 0.23/1.06 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1504868 completed with status 0
% 0.23/1.06 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.23/1.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/1.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/1.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/1.06 % No SInE strategy applied
% 0.23/1.06 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.23/1.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/1.06 % Starting SubtermCWHack with 136s (1) cores
% 0.23/1.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.23/1.06 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.23/1.06 % Starting new_bool_3 with 136s (1) cores
% 0.23/1.06 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.23/1.06 % G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 1504874 completed with status 0
% 0.23/1.06 % Result found by G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 0.23/1.06 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/1.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/1.06 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/1.06 % No SInE strategy applied
% 0.23/1.06 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.23/1.06 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/1.06 % Starting SubtermCWHack with 136s (1) cores
% 0.23/1.06 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.23/1.06 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.23/1.06 % Preprocessing time : 0.005 s
% 0.23/1.06 % Presaturation interreduction done
% 0.23/1.06
% 0.23/1.06 % Proof found!
% 0.23/1.06 % SZS status Theorem
% 0.23/1.06 % SZS output start CNFRefutation
% See solution above
% 0.23/1.06 % Parsed axioms : 53
% 0.23/1.06 % Removed by relevancy pruning/SinE : 0
% 0.23/1.06 % Initial clauses : 268
% 0.23/1.06 % Removed in clause preprocessing : 3
% 0.23/1.06 % Initial clauses in saturation : 265
% 0.23/1.06 % Processed clauses : 1072
% 0.23/1.06 % ...of these trivial : 23
% 0.23/1.06 % ...subsumed : 279
% 0.23/1.06 % ...remaining for further processing : 770
% 0.23/1.06 % Other redundant clauses eliminated : 33
% 0.23/1.06 % Clauses deleted for lack of memory : 0
% 0.23/1.06 % Backward-subsumed : 29
% 0.23/1.06 % Backward-rewritten : 218
% 0.23/1.06 % Generated clauses : 5645
% 0.23/1.06 % ...of the previous two non-redundant : 5461
% 0.23/1.06 % ...aggressively subsumed : 0
% 0.23/1.06 % Contextual simplify-reflections : 17
% 0.23/1.06 % Paramodulations : 5585
% 0.23/1.06 % Factorizations : 0
% 0.23/1.06 % NegExts : 0
% 0.23/1.06 % Equation resolutions : 60
% 0.23/1.06 % Disequality decompositions : 0
% 0.23/1.06 % Total rewrite steps : 5261
% 0.23/1.06 % ...of those cached : 5220
% 0.23/1.06 % Propositional unsat checks : 0
% 0.23/1.06 % Propositional check models : 0
% 0.23/1.06 % Propositional check unsatisfiable : 0
% 0.23/1.06 % Propositional clauses : 0
% 0.23/1.06 % Propositional clauses after purity: 0
% 0.23/1.06 % Propositional unsat core size : 0
% 0.23/1.06 % Propositional preprocessing time : 0.000
% 0.23/1.06 % Propositional encoding time : 0.000
% 0.23/1.06 % Propositional solver time : 0.000
% 0.23/1.06 % Success case prop preproc time : 0.000
% 0.23/1.06 % Success case prop encoding time : 0.000
% 0.23/1.06 % Success case prop solver time : 0.000
% 0.23/1.06 % Current number of processed clauses : 275
% 0.23/1.06 % Positive orientable unit clauses : 59
% 0.23/1.06 % Positive unorientable unit clauses: 0
% 0.23/1.06 % Negative unit clauses : 20
% 0.23/1.06 % Non-unit-clauses : 196
% 0.23/1.06 % Current number of unprocessed clauses: 4833
% 0.23/1.06 % ...number of literals in the above : 42288
% 0.23/1.06 % Current number of archived formulas : 0
% 0.23/1.06 % Current number of archived clauses : 494
% 0.23/1.06 % Clause-clause subsumption calls (NU) : 87964
% 0.23/1.06 % Rec. Clause-clause subsumption calls : 5711
% 0.23/1.06 % Non-unit clause-clause subsumptions : 210
% 0.23/1.06 % Unit Clause-clause subsumption calls : 3163
% 0.23/1.06 % Rewrite failures with RHS unbound : 0
% 0.23/1.06 % BW rewrite match attempts : 6
% 0.23/1.06 % BW rewrite match successes : 6
% 0.23/1.06 % Condensation attempts : 0
% 0.23/1.06 % Condensation successes : 0
% 0.23/1.06 % Termbank termtop insertions : 178756
% 0.23/1.06 % Search garbage collected termcells : 2512
% 0.23/1.06
% 0.23/1.06 % -------------------------------------------------
% 0.23/1.06 % User time : 0.235 s
% 0.23/1.06 % System time : 0.020 s
% 0.23/1.06 % Total time : 0.255 s
% 0.23/1.06 % Maximum resident set size: 4220 pages
% 0.23/1.06
% 0.23/1.06 % -------------------------------------------------
% 0.23/1.06 % User time : 0.937 s
% 0.23/1.06 % System time : 0.057 s
% 0.23/1.06 % Total time : 0.994 s
% 0.23/1.06 % Maximum resident set size: 4864 pages
% 0.23/1.06 % E exiting
%------------------------------------------------------------------------------