TSTP Solution File: NUM529+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM529+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 : 300s
% DateTime : Tue May 21 01:14:30 EDT 2024
% Result : ContradictoryAxioms 1.96s 0.83s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 98 ( 36 unt; 0 def)
% Number of atoms : 377 ( 149 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 455 ( 176 ~; 167 |; 72 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(m__3046,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(m__2963,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3)
& X1 != sz00
& X2 != sz00
& X3 != sz00 )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ isPrime0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(m__3124,hypothesis,
( xm != xn
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3124) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_21,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_22,plain,
! [X67,X68,X69] :
( ( aNaturalNumber0(X69)
| X69 != sdtsldt0(X68,X67)
| X67 = sz00
| ~ doDivides0(X67,X68)
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68) )
& ( X68 = sdtasdt0(X67,X69)
| X69 != sdtsldt0(X68,X67)
| X67 = sz00
| ~ doDivides0(X67,X68)
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X69)
| X68 != sdtasdt0(X67,X69)
| X69 = sdtsldt0(X68,X67)
| X67 = sz00
| ~ doDivides0(X67,X68)
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68) ) ),
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_20])])])])]) ).
fof(c_0_23,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X7,X8] :
( ~ aNaturalNumber0(X7)
| ~ aNaturalNumber0(X8)
| aNaturalNumber0(sdtasdt0(X7,X8)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_29,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDivAsso]) ).
cnf(c_0_30,hypothesis,
( sdtsldt0(X1,xp) = sdtasdt0(xm,xm)
| X1 != sdtasdt0(xn,xn)
| ~ doDivides0(xp,X1)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_31,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_35,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_37,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_38,plain,
! [X81,X82,X83] :
( ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| X81 = sz00
| ~ doDivides0(X81,X82)
| ~ aNaturalNumber0(X83)
| sdtasdt0(X83,sdtsldt0(X82,X81)) = sdtsldt0(sdtasdt0(X83,X82),X81) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_39,hypothesis,
( sdtsldt0(X1,xp) = sdtasdt0(xm,xm)
| X1 != sdtasdt0(xn,xn)
| ~ doDivides0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_40,hypothesis,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(split_conjunct,[status(thm)],[m__3046]) ).
fof(c_0_41,plain,
! [X17,X18,X19] :
( ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X19)
| sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_42,hypothesis,
( sdtasdt0(xp,X1) = xn
| X1 != xq ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_26]),c_0_36])]),c_0_27]) ).
cnf(c_0_43,hypothesis,
( aNaturalNumber0(X1)
| X1 != xq ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_35]),c_0_26]),c_0_36])]),c_0_27]) ).
fof(c_0_44,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_45,plain,
( X1 = sz00
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,hypothesis,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_47,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3)
& X1 != sz00
& X2 != sz00
& X3 != sz00 )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ isPrime0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[m__2963]) ).
fof(c_0_48,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
fof(c_0_49,plain,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_50,hypothesis,
( xm != xn
& sdtlseqdt0(xm,xn) ),
inference(fof_simplification,[status(thm)],[m__3124]) ).
cnf(c_0_51,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xp,xq) = xn,
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(xq),
inference(er,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X21] :
( ( sdtasdt0(X21,sz00) = sz00
| ~ aNaturalNumber0(X21) )
& ( sz00 = sdtasdt0(sz00,X21)
| ~ aNaturalNumber0(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
fof(c_0_55,plain,
! [X57,X58] :
( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X58)
| X57 = sz00
| sdtlseqdt0(X58,sdtasdt0(X58,X57)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
cnf(c_0_56,hypothesis,
( sdtsldt0(sdtasdt0(X1,xn),xp) = sdtasdt0(X1,xq)
| ~ 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_45,c_0_35]),c_0_34]),c_0_36]),c_0_26])]),c_0_27]) ).
cnf(c_0_57,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_36])]) ).
fof(c_0_58,hypothesis,
! [X92,X93,X94] :
( ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| X92 = sz00
| X93 = sz00
| X94 = sz00
| sdtasdt0(X94,sdtasdt0(X93,X93)) != sdtasdt0(X92,X92)
| ~ iLess0(X92,xn)
| ~ isPrime0(X94) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_59,plain,
! [X84,X85] :
( ( X84 != sz00
| ~ isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( X84 != sz10
| ~ isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( ~ aNaturalNumber0(X85)
| ~ doDivides0(X85,X84)
| X85 = sz10
| X85 = X84
| ~ isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( aNaturalNumber0(esk3_1(X84))
| X84 = sz00
| X84 = sz10
| isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( doDivides0(esk3_1(X84),X84)
| X84 = sz00
| X84 = sz10
| isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( esk3_1(X84) != sz10
| X84 = sz00
| X84 = sz10
| isPrime0(X84)
| ~ aNaturalNumber0(X84) )
& ( esk3_1(X84) != X84
| X84 = sz00
| X84 = sz10
| isPrime0(X84)
| ~ aNaturalNumber0(X84) ) ),
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_48])])])])])]) ).
fof(c_0_60,plain,
! [X61,X62] :
( ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X62)
| X61 = X62
| ~ sdtlseqdt0(X61,X62)
| iLess0(X61,X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
fof(c_0_61,hypothesis,
( xm != xn
& sdtlseqdt0(xm,xn) ),
inference(fof_nnf,[status(thm)],[c_0_50]) ).
fof(c_0_62,plain,
! [X15,X16] :
( ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X16)
| sdtasdt0(X15,X16) = sdtasdt0(X16,X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_63,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_26])]) ).
cnf(c_0_64,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_66,plain,
! [X35,X36,X38] :
( ( aNaturalNumber0(esk1_2(X35,X36))
| ~ sdtlseqdt0(X35,X36)
| ~ aNaturalNumber0(X35)
| ~ aNaturalNumber0(X36) )
& ( sdtpldt0(X35,esk1_2(X35,X36)) = X36
| ~ sdtlseqdt0(X35,X36)
| ~ aNaturalNumber0(X35)
| ~ aNaturalNumber0(X36) )
& ( ~ aNaturalNumber0(X38)
| sdtpldt0(X35,X38) != X36
| sdtlseqdt0(X35,X36)
| ~ aNaturalNumber0(X35)
| ~ aNaturalNumber0(X36) ) ),
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)],[mDefLE])])])])])]) ).
cnf(c_0_67,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_36])]) ).
cnf(c_0_69,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_70,hypothesis,
( X1 = sz00
| X2 = sz00
| X3 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,sdtasdt0(X2,X2)) != sdtasdt0(X1,X1)
| ~ iLess0(X1,xn)
| ~ isPrime0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_73,hypothesis,
sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,hypothesis,
xm != xn,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,hypothesis,
sdtasdt0(xp,sz00) = sdtasdt0(xn,sz00),
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_53])]) ).
fof(c_0_77,plain,
! [X31,X32] :
( ( X31 = sz00
| sdtpldt0(X31,X32) != sz00
| ~ aNaturalNumber0(X31)
| ~ aNaturalNumber0(X32) )
& ( X32 = sz00
| sdtpldt0(X31,X32) != sz00
| ~ aNaturalNumber0(X31)
| ~ aNaturalNumber0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_78,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_79,hypothesis,
sdtlseqdt0(xm,sdtasdt0(xn,xq)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_32])]),c_0_69]) ).
cnf(c_0_80,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_68]),c_0_32])]) ).
cnf(c_0_81,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_82,hypothesis,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X3,sdtasdt0(X2,X2)) != sdtasdt0(X1,X1)
| ~ isPrime0(X3)
| ~ iLess0(X1,xn)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_83,hypothesis,
iLess0(xm,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_36]),c_0_32])]),c_0_74]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_85,hypothesis,
sdtasdt0(xn,sz00) = sdtasdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_65]),c_0_26])]) ).
cnf(c_0_86,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(xm,esk1_2(xm,sdtasdt0(xn,xq))) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_32])]) ).
cnf(c_0_88,hypothesis,
aNaturalNumber0(esk1_2(xm,sdtasdt0(xn,xq))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_79]),c_0_80]),c_0_32])]) ).
cnf(c_0_89,hypothesis,
( X1 = sz00
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(xn,xq)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_68]),c_0_32])]),c_0_69]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xn,xq),
inference(rw,[status(thm)],[c_0_84,c_0_68]) ).
cnf(c_0_91,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_92,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(sz00,xp) = sdtasdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_85]),c_0_65]),c_0_36])]) ).
cnf(c_0_94,hypothesis,
sdtasdt0(xn,xq) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_32])]),c_0_69]) ).
cnf(c_0_95,hypothesis,
xq = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_26]),c_0_53])]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_26])]) ).
cnf(c_0_97,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_85]),c_0_93]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM529+1 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 06:24:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.96/0.83 # Version: 3.1.0
% 1.96/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.96/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.96/0.83 # Starting new_bool_3 with 300s (1) cores
% 1.96/0.83 # Starting new_bool_1 with 300s (1) cores
% 1.96/0.83 # Starting sh5l with 300s (1) cores
% 1.96/0.83 # sh5l with pid 13026 completed with status 8
% 1.96/0.83 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 13023 completed with status 0
% 1.96/0.83 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.96/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.96/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.96/0.83 # No SInE strategy applied
% 1.96/0.83 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.96/0.83 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.96/0.83 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 1.96/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.96/0.83 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 1.96/0.83 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 1.96/0.83 # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 1.96/0.83 # G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with pid 13038 completed with status 0
% 1.96/0.83 # Result found by G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S
% 1.96/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.96/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.96/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.96/0.83 # No SInE strategy applied
% 1.96/0.83 # Search class: FGHSF-FFMM21-SFFFFFNN
% 1.96/0.83 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.96/0.83 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 1.96/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.96/0.83 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 1.96/0.83 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 1.96/0.83 # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 1.96/0.83 # Preprocessing time : 0.002 s
% 1.96/0.83 # Presaturation interreduction done
% 1.96/0.83
% 1.96/0.83 # Proof found!
% 1.96/0.83 # SZS status ContradictoryAxioms
% 1.96/0.83 # SZS output start CNFRefutation
% See solution above
% 1.96/0.83 # Parsed axioms : 48
% 1.96/0.83 # Removed by relevancy pruning/SinE : 0
% 1.96/0.83 # Initial clauses : 87
% 1.96/0.83 # Removed in clause preprocessing : 4
% 1.96/0.83 # Initial clauses in saturation : 83
% 1.96/0.83 # Processed clauses : 1323
% 1.96/0.83 # ...of these trivial : 31
% 1.96/0.83 # ...subsumed : 468
% 1.96/0.83 # ...remaining for further processing : 824
% 1.96/0.83 # Other redundant clauses eliminated : 29
% 1.96/0.83 # Clauses deleted for lack of memory : 0
% 1.96/0.83 # Backward-subsumed : 109
% 1.96/0.83 # Backward-rewritten : 403
% 1.96/0.83 # Generated clauses : 5692
% 1.96/0.83 # ...of the previous two non-redundant : 5396
% 1.96/0.83 # ...aggressively subsumed : 0
% 1.96/0.83 # Contextual simplify-reflections : 86
% 1.96/0.83 # Paramodulations : 5611
% 1.96/0.83 # Factorizations : 4
% 1.96/0.83 # NegExts : 0
% 1.96/0.83 # Equation resolutions : 70
% 1.96/0.83 # Disequality decompositions : 0
% 1.96/0.83 # Total rewrite steps : 11960
% 1.96/0.83 # ...of those cached : 11855
% 1.96/0.83 # Propositional unsat checks : 0
% 1.96/0.83 # Propositional check models : 0
% 1.96/0.83 # Propositional check unsatisfiable : 0
% 1.96/0.83 # Propositional clauses : 0
% 1.96/0.83 # Propositional clauses after purity: 0
% 1.96/0.83 # Propositional unsat core size : 0
% 1.96/0.83 # Propositional preprocessing time : 0.000
% 1.96/0.83 # Propositional encoding time : 0.000
% 1.96/0.83 # Propositional solver time : 0.000
% 1.96/0.83 # Success case prop preproc time : 0.000
% 1.96/0.83 # Success case prop encoding time : 0.000
% 1.96/0.83 # Success case prop solver time : 0.000
% 1.96/0.83 # Current number of processed clauses : 226
% 1.96/0.83 # Positive orientable unit clauses : 77
% 1.96/0.83 # Positive unorientable unit clauses: 0
% 1.96/0.83 # Negative unit clauses : 15
% 1.96/0.83 # Non-unit-clauses : 134
% 1.96/0.83 # Current number of unprocessed clauses: 3782
% 1.96/0.83 # ...number of literals in the above : 18305
% 1.96/0.83 # Current number of archived formulas : 0
% 1.96/0.83 # Current number of archived clauses : 597
% 1.96/0.83 # Clause-clause subsumption calls (NU) : 185881
% 1.96/0.83 # Rec. Clause-clause subsumption calls : 5900
% 1.96/0.83 # Non-unit clause-clause subsumptions : 619
% 1.96/0.83 # Unit Clause-clause subsumption calls : 7734
% 1.96/0.83 # Rewrite failures with RHS unbound : 0
% 1.96/0.83 # BW rewrite match attempts : 32
% 1.96/0.83 # BW rewrite match successes : 31
% 1.96/0.83 # Condensation attempts : 0
% 1.96/0.83 # Condensation successes : 0
% 1.96/0.83 # Termbank termtop insertions : 193693
% 1.96/0.83 # Search garbage collected termcells : 1409
% 1.96/0.83
% 1.96/0.83 # -------------------------------------------------
% 1.96/0.83 # User time : 0.311 s
% 1.96/0.83 # System time : 0.006 s
% 1.96/0.83 # Total time : 0.318 s
% 1.96/0.83 # Maximum resident set size: 1968 pages
% 1.96/0.83
% 1.96/0.83 # -------------------------------------------------
% 1.96/0.83 # User time : 1.497 s
% 1.96/0.83 # System time : 0.065 s
% 1.96/0.83 # Total time : 1.562 s
% 1.96/0.83 # Maximum resident set size: 1740 pages
% 1.96/0.83 % E---3.1 exiting
% 1.96/0.84 % E exiting
%------------------------------------------------------------------------------