TSTP Solution File: NUM528+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n007.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 09:33:26 EDT 2022
% Result : Theorem 0.25s 1.42s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 102 ( 29 unt; 0 def)
% Number of atoms : 336 ( 130 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 382 ( 148 ~; 152 |; 60 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 98 ( 0 sgn 53 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETotal) ).
fof(m__,conjecture,
( xm != xn
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xn )
| sdtlseqdt0(xm,xn) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__2987) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsB_02) ).
fof(m__3152,hypothesis,
( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xm )
| sdtlseqdt0(xn,xm) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
& sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3152) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_AddZero) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3082) ).
fof(m__3046,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3046) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mZeroMul) ).
fof(m__3059,hypothesis,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3059) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddComm) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3014) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mZeroAdd) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETran) ).
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/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulCanc) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_MulUnit) ).
fof(m__3025,hypothesis,
( xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3025) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLEAsym) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC_01) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulComm) ).
fof(c_0_22,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_23,negated_conjecture,
~ ( xm != xn
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xn )
| sdtlseqdt0(xm,xn) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_24,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_26,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_27,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| sdtpldt0(xm,X2) != xn
| xm = xn )
& ( ~ sdtlseqdt0(xm,xn)
| xm = xn ) ),
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_23])])])])])]) ).
cnf(c_0_28,hypothesis,
( sdtlseqdt0(xm,X1)
| sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_30,hypothesis,
! [X2] :
( ( aNaturalNumber0(esk9_0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(xn,X2) != xm )
& ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
| ~ aNaturalNumber0(X2)
| sdtpldt0(xn,X2) != xm )
& ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X2)
| sdtpldt0(xn,X2) != xm )
& ( aNaturalNumber0(esk9_0)
| ~ sdtlseqdt0(xn,xm) )
& ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
| ~ sdtlseqdt0(xn,xm) )
& ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(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__3152])])])])])])]) ).
fof(c_0_31,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_32,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_35,hypothesis,
( aNaturalNumber0(esk7_0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(esk8_0)
& xn = sdtasdt0(xp,esk8_0)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__3046])])])]) ).
cnf(c_0_36,negated_conjecture,
( xm = xn
| ~ sdtlseqdt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,hypothesis,
( sdtlseqdt0(xn,xm)
| sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,hypothesis,
( aNaturalNumber0(esk9_0)
| sdtpldt0(xn,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_41,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_42,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
fof(c_0_44,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,hypothesis,
( aNaturalNumber0(esk9_0)
| ~ sdtlseqdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_48,negated_conjecture,
( xm = xn
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,hypothesis,
( aNaturalNumber0(esk9_0)
| xm != xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_29])]) ).
cnf(c_0_50,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_52,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_43])]) ).
fof(c_0_54,plain,
! [X3,X4] :
( ( X3 = sz00
| sdtpldt0(X3,X4) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( X4 = sz00
| sdtpldt0(X3,X4) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
| ~ sdtlseqdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_56,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_46]),c_0_34])]) ).
cnf(c_0_58,hypothesis,
aNaturalNumber0(esk9_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_59,hypothesis,
( sdtasdt0(xm,xm) = sz00
| sdtasdt0(xn,xn) != sz00 ),
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_50,c_0_51]),c_0_34])]),c_0_52]),c_0_53])]) ).
cnf(c_0_60,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_61,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_62,plain,
( X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_63,hypothesis,
( sdtpldt0(esk9_0,sdtasdt0(xn,xn)) = sdtasdt0(xm,xm)
| ~ sdtlseqdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_64,hypothesis,
sdtasdt0(xn,xn) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_59]),c_0_25])]),c_0_60]) ).
cnf(c_0_65,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,hypothesis,
( sdtlseqdt0(xn,X1)
| sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_67,hypothesis,
( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
| sdtpldt0(xn,X1) != xm
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_68,hypothesis,
( sdtasdt0(xm,xm) != sz00
| ~ sdtlseqdt0(xn,xm) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_58]),c_0_57])]),c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( xm = xn
| sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_29]),c_0_25])]) ).
cnf(c_0_70,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_66,c_0_29]) ).
fof(c_0_71,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_72,plain,
( X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_73,hypothesis,
( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
| xm != xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_39]),c_0_40]),c_0_29])]) ).
cnf(c_0_74,negated_conjecture,
( xm = xn
| sdtasdt0(xm,xm) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_29])]) ).
cnf(c_0_75,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,hypothesis,
sdtasdt0(xm,xm) != sz00,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_57])]),c_0_58])]),c_0_64]),c_0_74]) ).
fof(c_0_77,plain,
! [X2] :
( ( sdtasdt0(X2,sz10) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtasdt0(sz10,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_78,hypothesis,
! [X3,X4] :
( 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) ),
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)],[m__3025])])])])])]) ).
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_71]) ).
fof(c_0_80,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_81,hypothesis,
( X1 = xp
| sdtasdt0(X1,sdtasdt0(xm,xm)) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_51]),c_0_34])]),c_0_53])]),c_0_76]) ).
cnf(c_0_82,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_84,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,hypothesis,
( X1 = esk7_0
| sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
| ~ 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_45]),c_0_46]),c_0_34])]),c_0_52]) ).
fof(c_0_86,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| X3 = sz00
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_87,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_88,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,hypothesis,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_90,hypothesis,
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_81,c_0_82]),c_0_83]),c_0_53])]),c_0_84]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_53])]) ).
cnf(c_0_92,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,hypothesis,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_57]),c_0_53])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(xn,xn) != esk7_0,
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,hypothesis,
( ~ sdtlseqdt0(esk7_0,sdtasdt0(xn,xn))
| ~ sdtlseqdt0(xn,xm) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_91]),c_0_91]),c_0_95]) ).
cnf(c_0_98,hypothesis,
sdtlseqdt0(esk7_0,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_96,c_0_45]),c_0_34]),c_0_46])]),c_0_52]) ).
cnf(c_0_99,hypothesis,
~ sdtlseqdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_100,negated_conjecture,
xm = xn,
inference(sr,[status(thm)],[c_0_48,c_0_99]) ).
cnf(c_0_101,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_ET %s %d
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jul 7 12:17:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.25/1.42 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.25/1.42 # Preprocessing time : 0.020 s
% 0.25/1.42
% 0.25/1.42 # Proof found!
% 0.25/1.42 # SZS status Theorem
% 0.25/1.42 # SZS output start CNFRefutation
% See solution above
% 0.25/1.42 # Proof object total steps : 102
% 0.25/1.42 # Proof object clause steps : 63
% 0.25/1.42 # Proof object formula steps : 39
% 0.25/1.42 # Proof object conjectures : 8
% 0.25/1.42 # Proof object clause conjectures : 5
% 0.25/1.42 # Proof object formula conjectures : 3
% 0.25/1.42 # Proof object initial clauses used : 33
% 0.25/1.42 # Proof object initial formulas used : 22
% 0.25/1.42 # Proof object generating inferences : 25
% 0.25/1.42 # Proof object simplifying inferences : 73
% 0.25/1.42 # Training examples: 0 positive, 0 negative
% 0.25/1.42 # Parsed axioms : 48
% 0.25/1.42 # Removed by relevancy pruning/SinE : 0
% 0.25/1.42 # Initial clauses : 107
% 0.25/1.42 # Removed in clause preprocessing : 3
% 0.25/1.42 # Initial clauses in saturation : 104
% 0.25/1.42 # Processed clauses : 1200
% 0.25/1.42 # ...of these trivial : 11
% 0.25/1.42 # ...subsumed : 620
% 0.25/1.42 # ...remaining for further processing : 569
% 0.25/1.42 # Other redundant clauses eliminated : 41
% 0.25/1.42 # Clauses deleted for lack of memory : 0
% 0.25/1.42 # Backward-subsumed : 55
% 0.25/1.42 # Backward-rewritten : 204
% 0.25/1.42 # Generated clauses : 3874
% 0.25/1.42 # ...of the previous two non-trivial : 3588
% 0.25/1.42 # Contextual simplify-reflections : 203
% 0.25/1.42 # Paramodulations : 3801
% 0.25/1.42 # Factorizations : 1
% 0.25/1.42 # Equation resolutions : 69
% 0.25/1.42 # Current number of processed clauses : 306
% 0.25/1.42 # Positive orientable unit clauses : 36
% 0.25/1.42 # Positive unorientable unit clauses: 0
% 0.25/1.42 # Negative unit clauses : 19
% 0.25/1.42 # Non-unit-clauses : 251
% 0.25/1.42 # Current number of unprocessed clauses: 1339
% 0.25/1.42 # ...number of literals in the above : 8218
% 0.25/1.42 # Current number of archived formulas : 0
% 0.25/1.42 # Current number of archived clauses : 262
% 0.25/1.42 # Clause-clause subsumption calls (NU) : 45619
% 0.25/1.42 # Rec. Clause-clause subsumption calls : 14494
% 0.25/1.42 # Non-unit clause-clause subsumptions : 668
% 0.25/1.42 # Unit Clause-clause subsumption calls : 2041
% 0.25/1.42 # Rewrite failures with RHS unbound : 0
% 0.25/1.42 # BW rewrite match attempts : 20
% 0.25/1.42 # BW rewrite match successes : 20
% 0.25/1.42 # Condensation attempts : 0
% 0.25/1.42 # Condensation successes : 0
% 0.25/1.42 # Termbank termtop insertions : 69556
% 0.25/1.42
% 0.25/1.42 # -------------------------------------------------
% 0.25/1.42 # User time : 0.124 s
% 0.25/1.42 # System time : 0.004 s
% 0.25/1.42 # Total time : 0.128 s
% 0.25/1.42 # Maximum resident set size: 6036 pages
% 0.25/23.41 eprover: CPU time limit exceeded, terminating
% 0.25/23.42 eprover: CPU time limit exceeded, terminating
% 0.25/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.43 eprover: No such file or directory
% 0.25/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.43 eprover: No such file or directory
% 0.25/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.44 eprover: No such file or directory
% 0.25/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.44 eprover: No such file or directory
% 0.25/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.44 eprover: No such file or directory
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.46 eprover: No such file or directory
% 0.25/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.46 eprover: No such file or directory
% 0.25/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.46 eprover: No such file or directory
% 0.25/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.46 eprover: No such file or directory
% 0.25/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47 eprover: No such file or directory
% 0.25/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.47 eprover: No such file or directory
% 0.25/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.49 eprover: No such file or directory
%------------------------------------------------------------------------------