TSTP Solution File: NUM516+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM516+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.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 09:33:18 EDT 2022
% Result : Theorem 0.74s 69.94s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 21 unt; 0 def)
% Number of atoms : 302 ( 120 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 351 ( 125 ~; 132 |; 77 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__) ).
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__2504,hypothesis,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__2504) ).
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/sandbox2/solver/bin/../tmp/theBenchmark.p',m__2342) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddAsso) ).
fof(m__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__2487) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__1837) ).
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(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMonAdd) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsB) ).
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(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddCanc) ).
fof(c_0_12,negated_conjecture,
~ ( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_13,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])])])])])]) ).
fof(c_0_14,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) != xn
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(esk19_0)
& sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
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__2504])])])])]) ).
fof(c_0_15,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_16,negated_conjecture,
! [X2] :
( ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X2) != sdtpldt0(sdtpldt0(xn,xm),xp)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X2) != sdtpldt0(sdtpldt0(xn,xm),xp)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X2) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),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_12])])])])])]) ).
fof(c_0_17,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_18,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__2487])])])]) ).
cnf(c_0_24,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
( X1 = sdtsldt0(xn,xr)
| sdtasdt0(xr,X1) != 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_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_30,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_33,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_34,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X6,X4) != sdtpldt0(X6,X5)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) != sdtpldt0(X5,X6)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
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)],[mMonAdd])])])])])]) ).
cnf(c_0_35,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,hypothesis,
sdtsldt0(xn,xr) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_37,hypothesis,
sdtsldt0(xn,xr) != xn,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_26]),c_0_27]),c_0_20])]) ).
cnf(c_0_39,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( X2 = X1
| sdtlseqdt0(sdtpldt0(X2,X3),sdtpldt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,hypothesis,
esk18_0 != xn,
inference(rw,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]),c_0_27])]) ).
cnf(c_0_44,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(esk18_0,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_36]),c_0_36]) ).
cnf(c_0_45,hypothesis,
( sdtlseqdt0(sdtpldt0(esk18_0,X1),sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_31]),c_0_28])]),c_0_42]) ).
fof(c_0_46,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_47,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(esk18_0,sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_36]),c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_20])]) ).
cnf(c_0_49,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_26]),c_0_27])]) ).
cnf(c_0_50,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ aNaturalNumber0(sdtpldt0(xp,xm)) ),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_26]),c_0_27])]) ).
cnf(c_0_54,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_26]),c_0_27]),c_0_20])]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(esk18_0,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_26]),c_0_27])]) ).
cnf(c_0_56,negated_conjecture,
sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_27]),c_0_26])]) ).
cnf(c_0_57,negated_conjecture,
( sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_58,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(esk18_0,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_36]),c_0_36]) ).
fof(c_0_59,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])])]) ).
cnf(c_0_60,negated_conjecture,
( aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_55]),c_0_31])]) ).
cnf(c_0_61,negated_conjecture,
( aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xp,xm)))
| ~ aNaturalNumber0(sdtpldt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_56]),c_0_31])]) ).
cnf(c_0_62,negated_conjecture,
( sdtpldt0(esk18_0,sdtpldt0(xp,xm)) = sdtpldt0(xn,sdtpldt0(xm,xp))
| ~ sdtlseqdt0(sdtpldt0(esk18_0,sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_36]),c_0_36]) ).
cnf(c_0_63,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xp,xm))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_55]),c_0_55]) ).
cnf(c_0_64,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_51]),c_0_26]),c_0_27])]) ).
cnf(c_0_66,negated_conjecture,
aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xp,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51]),c_0_27]),c_0_26])]) ).
fof(c_0_67,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X4,X5) != sdtpldt0(X4,X6)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtpldt0(X5,X4) != sdtpldt0(X6,X4)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_68,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_56]),c_0_56]) ).
cnf(c_0_69,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm))
| sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xp,xm)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
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_66])]) ).
cnf(c_0_70,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_71,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( X1 = xn
| sdtpldt0(X1,sdtpldt0(xm,xp)) != sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_28])]) ).
cnf(c_0_73,negated_conjecture,
( X1 = xn
| sdtpldt0(X1,sdtpldt0(xm,xp)) != sdtpldt0(xn,sdtpldt0(xp,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_51]),c_0_26]),c_0_27])]) ).
cnf(c_0_74,negated_conjecture,
sdtpldt0(esk18_0,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(rw,[status(thm)],[c_0_55,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_31])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM516+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n004.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 : Tue Jul 5 14:42:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.39/23.41 eprover: CPU time limit exceeded, terminating
% 0.39/23.42 eprover: CPU time limit exceeded, terminating
% 0.39/23.42 eprover: CPU time limit exceeded, terminating
% 0.39/23.43 eprover: CPU time limit exceeded, terminating
% 0.55/46.43 eprover: CPU time limit exceeded, terminating
% 0.55/46.44 eprover: CPU time limit exceeded, terminating
% 0.55/46.44 eprover: CPU time limit exceeded, terminating
% 0.55/46.44 eprover: CPU time limit exceeded, terminating
% 0.74/69.45 eprover: CPU time limit exceeded, terminating
% 0.74/69.46 eprover: CPU time limit exceeded, terminating
% 0.74/69.47 eprover: CPU time limit exceeded, terminating
% 0.74/69.47 eprover: CPU time limit exceeded, terminating
% 0.74/69.94 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.74/69.94
% 0.74/69.94 # Failure: Resource limit exceeded (time)
% 0.74/69.94 # OLD status Res
% 0.74/69.94 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.74/69.94 # Preprocessing time : 0.020 s
% 0.74/69.94 # Running protocol protocol_eprover_230b6c199cce1dcf6700db59e75a93feb83d1bd9 for 23 seconds:
% 0.74/69.94
% 0.74/69.94 # Failure: Resource limit exceeded (time)
% 0.74/69.94 # OLD status Res
% 0.74/69.94 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,01,20000,1.0)
% 0.74/69.94 # Preprocessing time : 0.014 s
% 0.74/69.94 # Running protocol protocol_eprover_48e494e00e0717ec2eabf59b73b2d711334607de for 23 seconds:
% 0.74/69.94
% 0.74/69.94 # Failure: Resource limit exceeded (time)
% 0.74/69.94 # OLD status Res
% 0.74/69.94 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,03,20000,1.0)
% 0.74/69.94 # Preprocessing time : 0.020 s
% 0.74/69.94 # Running protocol protocol_eprover_33aa8a325940064c53b389b41203bb48a5cb5006 for 23 seconds:
% 0.74/69.94 # Preprocessing time : 0.028 s
% 0.74/69.94
% 0.74/69.94 # Proof found!
% 0.74/69.94 # SZS status Theorem
% 0.74/69.94 # SZS output start CNFRefutation
% See solution above
% 0.74/69.94 # Proof object total steps : 76
% 0.74/69.94 # Proof object clause steps : 52
% 0.74/69.94 # Proof object formula steps : 24
% 0.74/69.94 # Proof object conjectures : 32
% 0.74/69.94 # Proof object clause conjectures : 29
% 0.74/69.94 # Proof object formula conjectures : 3
% 0.74/69.94 # Proof object initial clauses used : 19
% 0.74/69.94 # Proof object initial formulas used : 12
% 0.74/69.94 # Proof object generating inferences : 24
% 0.74/69.94 # Proof object simplifying inferences : 81
% 0.74/69.94 # Training examples: 0 positive, 0 negative
% 0.74/69.94 # Parsed axioms : 55
% 0.74/69.94 # Removed by relevancy pruning/SinE : 0
% 0.74/69.94 # Initial clauses : 281
% 0.74/69.94 # Removed in clause preprocessing : 3
% 0.74/69.94 # Initial clauses in saturation : 278
% 0.74/69.94 # Processed clauses : 1850
% 0.74/69.94 # ...of these trivial : 88
% 0.74/69.94 # ...subsumed : 654
% 0.74/69.94 # ...remaining for further processing : 1108
% 0.74/69.94 # Other redundant clauses eliminated : 9
% 0.74/69.94 # Clauses deleted for lack of memory : 0
% 0.74/69.94 # Backward-subsumed : 93
% 0.74/69.94 # Backward-rewritten : 184
% 0.74/69.94 # Generated clauses : 11322
% 0.74/69.94 # ...of the previous two non-trivial : 10508
% 0.74/69.94 # Contextual simplify-reflections : 0
% 0.74/69.94 # Paramodulations : 11201
% 0.74/69.94 # Factorizations : 2
% 0.74/69.94 # Equation resolutions : 116
% 0.74/69.94 # Current number of processed clauses : 827
% 0.74/69.94 # Positive orientable unit clauses : 222
% 0.74/69.94 # Positive unorientable unit clauses: 0
% 0.74/69.94 # Negative unit clauses : 34
% 0.74/69.94 # Non-unit-clauses : 571
% 0.74/69.94 # Current number of unprocessed clauses: 6542
% 0.74/69.94 # ...number of literals in the above : 47239
% 0.74/69.94 # Current number of archived formulas : 0
% 0.74/69.94 # Current number of archived clauses : 280
% 0.74/69.94 # Clause-clause subsumption calls (NU) : 27965
% 0.74/69.94 # Rec. Clause-clause subsumption calls : 13672
% 0.74/69.94 # Non-unit clause-clause subsumptions : 619
% 0.74/69.94 # Unit Clause-clause subsumption calls : 11193
% 0.74/69.94 # Rewrite failures with RHS unbound : 0
% 0.74/69.94 # BW rewrite match attempts : 222
% 0.74/69.94 # BW rewrite match successes : 63
% 0.74/69.94 # Condensation attempts : 0
% 0.74/69.94 # Condensation successes : 0
% 0.74/69.94 # Termbank termtop insertions : 371712
% 0.74/69.94
% 0.74/69.94 # -------------------------------------------------
% 0.74/69.94 # User time : 0.258 s
% 0.74/69.94 # System time : 0.010 s
% 0.74/69.94 # Total time : 0.268 s
% 0.74/69.94 # Maximum resident set size: 11636 pages
% 0.74/92.47 eprover: CPU time limit exceeded, terminating
% 0.74/92.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.48 eprover: No such file or directory
% 0.74/92.49 eprover: CPU time limit exceeded, terminating
% 0.74/92.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.49 eprover: No such file or directory
% 0.74/92.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.49 eprover: No such file or directory
% 0.74/92.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.49 eprover: No such file or directory
% 0.74/92.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.50 eprover: No such file or directory
% 0.74/92.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.50 eprover: No such file or directory
% 0.74/92.50 eprover: CPU time limit exceeded, terminating
% 0.74/92.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.50 eprover: No such file or directory
% 0.74/92.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.50 eprover: No such file or directory
% 0.74/92.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.51 eprover: No such file or directory
% 0.74/92.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.51 eprover: No such file or directory
% 0.74/92.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.51 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.52 eprover: No such file or directory
% 0.74/92.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.53 eprover: No such file or directory
% 0.74/92.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.74/92.53 eprover: No such file or directory
% 0.74/92.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.53 eprover: No such file or directory
% 0.74/92.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.54 eprover: No such file or directory
% 0.74/92.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.54 eprover: No such file or directory
% 0.74/92.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.55 eprover: No such file or directory
% 0.74/92.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.74/92.55 eprover: No such file or directory
%------------------------------------------------------------------------------