%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM502+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:33:08 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 99 ( 28 unt; 0 def)
% Number of atoms : 406 ( 149 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 492 ( 185 ~; 192 |; 95 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 53 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mLETotal) ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1860) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2342) ).
fof(m__,conjecture,
( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2306) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mSortsB) ).
fof(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2362) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1837) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mLETran) ).
fof(m__2075,hypothesis,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xm )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2075) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mLEAsym) ).
fof(m__2287,hypothesis,
( xn != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2287) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mMonMul) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mSortsB_02) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mMulCanc) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2315) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mZeroMul) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m_MulZero) ).
fof(c_0_19,plain,
! [X3,X4] :
( ( X4 != X3
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_20,hypothesis,
! [X3,X4] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X4)
| xp != sdtasdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| X3 = sz10
| X3 = xp )
& ( ~ doDivides0(X3,xp)
| ~ aNaturalNumber0(X3)
| X3 = sz10
| X3 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])])])]) ).
fof(c_0_21,hypothesis,
! [X4,X5] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X5)
| xr != sdtasdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| X4 = sz10
| X4 = xr )
& ( ~ doDivides0(X4,xr)
| ~ aNaturalNumber0(X4)
| X4 = sz10
| X4 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])])])]) ).
fof(c_0_22,negated_conjecture,
~ ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_23,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_25,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk1_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,esk1_2(X4,X5)) = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| sdtpldt0(X4,X7) != X5
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])])]) ).
fof(c_0_26,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_27,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__2362])])])]) ).
cnf(c_0_28,hypothesis,
( X1 = xp
| X1 = sz10
| ~ aNaturalNumber0(X1)
| xp != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
xk = sdtasdt0(xr,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,hypothesis,
xr != sz10,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_33,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| sdtpldt0(xk,X2) != xp
| xk = xp )
& ( ~ sdtlseqdt0(xk,xp)
| xk = xp ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])])]) ).
cnf(c_0_34,hypothesis,
( sdtlseqdt0(xk,X1)
| sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_36,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,hypothesis,
sdtpldt0(xr,esk13_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,hypothesis,
( xr = xp
| xk != xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,hypothesis,
( sdtlseqdt0(xp,xk)
| sdtlseqdt0(xk,xp) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_36]),c_0_37]) ).
cnf(c_0_44,hypothesis,
( sdtpldt0(xp,esk13_0) = xk
| xk != xp ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_46,negated_conjecture,
( xk = xp
| sdtlseqdt0(xp,xk) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_47,hypothesis,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| sdtpldt0(xp,X2) != xm )
& ~ sdtlseqdt0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2075])])])])]) ).
fof(c_0_48,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_49,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,hypothesis,
sdtlseqdt0(xp,xk),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_35])]),c_0_46]) ).
cnf(c_0_51,hypothesis,
( sdtpldt0(xp,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( sdtpldt0(X2,esk1_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,hypothesis,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_35]),c_0_24])]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_56,hypothesis,
( xn != xp
& aNaturalNumber0(esk10_0)
& sdtpldt0(xn,esk10_0) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(esk11_0)
& sdtpldt0(xm,esk11_0) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__2287])])])]) ).
cnf(c_0_57,hypothesis,
( X1 != xm
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(esk1_2(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_35])]) ).
cnf(c_0_58,plain,
( aNaturalNumber0(esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_59,hypothesis,
( sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
fof(c_0_60,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,X5) != sdtasdt0(X4,X6)
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtasdt0(X5,X4) != sdtasdt0(X6,X4)
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
fof(c_0_61,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_62,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,X5) != sdtasdt0(X4,X6)
| X5 = X6
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| X4 = sz00
| ~ aNaturalNumber0(X4) )
& ( sdtasdt0(X5,X4) != sdtasdt0(X6,X4)
| X5 = X6
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| X4 = sz00
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])])])]) ).
cnf(c_0_63,hypothesis,
( xk = X1
| ~ sdtlseqdt0(xk,X1)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_24])]) ).
cnf(c_0_64,hypothesis,
( sdtlseqdt0(xm,xk)
| sdtlseqdt0(xk,xm) ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_65,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,hypothesis,
( X1 != xm
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_35])]) ).
cnf(c_0_67,hypothesis,
sdtlseqdt0(xp,xp),
inference(spm,[status(thm)],[c_0_59,c_0_35]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_69,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_70,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_75,hypothesis,
( xk = xm
| sdtlseqdt0(xm,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_55])]) ).
cnf(c_0_76,hypothesis,
xk != xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_54]),c_0_24]),c_0_67]),c_0_35])]) ).
fof(c_0_77,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
fof(c_0_78,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) != sz00
| X3 = sz00
| X4 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_79,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xp,esk9_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_81,hypothesis,
aNaturalNumber0(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_82,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_83,plain,
( X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_70]),c_0_71]),c_0_71]),c_0_72]) ).
cnf(c_0_84,hypothesis,
( xn = sz00
| X1 = xm
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_69]),c_0_74]),c_0_55])]) ).
cnf(c_0_85,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_86,hypothesis,
sdtlseqdt0(xm,xk),
inference(sr,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_89,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_90,hypothesis,
( X1 = esk9_0
| sdtasdt0(xp,X1) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_35])]),c_0_82]) ).
fof(c_0_91,plain,
! [X2] :
( ( sdtasdt0(X2,sz00) = sz00
| ~ aNaturalNumber0(X2) )
& ( sz00 = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_92,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_24]),c_0_74]),c_0_35]),c_0_86])]),c_0_87]),c_0_88]),c_0_76]) ).
cnf(c_0_93,hypothesis,
( esk9_0 = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_80]),c_0_35]),c_0_81])]),c_0_82]) ).
cnf(c_0_94,hypothesis,
esk9_0 = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_90]),c_0_24])]) ).
cnf(c_0_95,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(sz00,xm) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_69,c_0_92]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_87]) ).
cnf(c_0_98,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_55])]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM502+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 10:12:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.23/1.42 # Preprocessing time : 0.026 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 99
% 0.23/1.42 # Proof object clause steps : 62
% 0.23/1.42 # Proof object formula steps : 37
% 0.23/1.42 # Proof object conjectures : 5
% 0.23/1.42 # Proof object clause conjectures : 2
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 35
% 0.23/1.42 # Proof object initial formulas used : 19
% 0.23/1.42 # Proof object generating inferences : 23
% 0.23/1.42 # Proof object simplifying inferences : 58
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 50
% 0.23/1.42 # Removed by relevancy pruning/SinE : 0
% 0.23/1.42 # Initial clauses : 242
% 0.23/1.42 # Removed in clause preprocessing : 3
% 0.23/1.42 # Initial clauses in saturation : 239
% 0.23/1.42 # Processed clauses : 2460
% 0.23/1.42 # ...of these trivial : 94
% 0.23/1.42 # ...subsumed : 1240
% 0.23/1.42 # ...remaining for further processing : 1126
% 0.23/1.42 # Other redundant clauses eliminated : 101
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 95
% 0.23/1.42 # Backward-rewritten : 317
% 0.23/1.42 # Generated clauses : 24176
% 0.23/1.42 # ...of the previous two non-trivial : 23057
% 0.23/1.42 # Contextual simplify-reflections : 485
% 0.23/1.42 # Paramodulations : 24013
% 0.23/1.42 # Factorizations : 10
% 0.23/1.42 # Equation resolutions : 149
% 0.23/1.42 # Current number of processed clauses : 709
% 0.23/1.42 # Positive orientable unit clauses : 90
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 37
% 0.23/1.42 # Non-unit-clauses : 582
% 0.23/1.42 # Current number of unprocessed clauses: 8486
% 0.23/1.42 # ...number of literals in the above : 50465
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 416
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 310892
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 67700
% 0.23/1.42 # Non-unit clause-clause subsumptions : 1315
% 0.23/1.42 # Unit Clause-clause subsumption calls : 16162
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 34
% 0.23/1.42 # BW rewrite match successes : 34
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 640954
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.530 s
% 0.23/1.42 # System time : 0.014 s
% 0.23/1.42 # Total time : 0.544 s
% 0.23/1.42 # Maximum resident set size: 24008 pages
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------