TSTP Solution File: NUM501+3 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.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 0.35s 23.54s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 155 ( 51 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 181 ( 65 ~; 62 |; 47 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 26 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p',mMulAsso) ).
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(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mDefDiv) ).
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(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mMulComm) ).
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__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(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1837) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_10,hypothesis,
! [X4,X5] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk8_0)
& xk = sdtasdt0(xr,esk8_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_11,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk9_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,esk9_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| X5 != sdtasdt0(X4,X7)
| doDivides0(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)],[mDefDiv])])])])])])]) ).
cnf(c_0_12,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
xk = sdtasdt0(xr,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
( sdtasdt0(xr,sdtasdt0(esk8_0,X1)) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
fof(c_0_18,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_19,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_20,hypothesis,
( doDivides0(xr,X1)
| X1 != sdtasdt0(xk,X2)
| ~ aNaturalNumber0(sdtasdt0(esk8_0,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15])]) ).
cnf(c_0_21,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_23,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(esk5_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_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_24,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X2) )
& ~ doDivides0(xr,sdtasdt0(xn,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)],[c_0_19])])])])]) ).
cnf(c_0_25,hypothesis,
( doDivides0(xr,X1)
| X1 != sdtasdt0(xk,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14])]) ).
cnf(c_0_26,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_30,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
( doDivides0(xr,X1)
| X1 != sdtasdt0(X2,xk)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xp,esk5_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_35,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xp,xk)),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_36,hypothesis,
( doDivides0(xr,sdtasdt0(X1,xk))
| ~ aNaturalNumber0(sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n021.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 : Fri Jul 8 00:36:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.35/23.41 eprover: CPU time limit exceeded, terminating
% 0.35/23.41 eprover: CPU time limit exceeded, terminating
% 0.35/23.42 eprover: CPU time limit exceeded, terminating
% 0.35/23.43 eprover: CPU time limit exceeded, terminating
% 0.35/23.54 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.35/23.54
% 0.35/23.54 # Failure: Resource limit exceeded (time)
% 0.35/23.54 # OLD status Res
% 0.35/23.54 # Preprocessing time : 0.026 s
% 0.35/23.54 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.35/23.54 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.35/23.54 # Preprocessing time : 0.015 s
% 0.35/23.54
% 0.35/23.54 # Proof found!
% 0.35/23.54 # SZS status Theorem
% 0.35/23.54 # SZS output start CNFRefutation
% See solution above
% 0.35/23.54 # Proof object total steps : 39
% 0.35/23.54 # Proof object clause steps : 22
% 0.35/23.54 # Proof object formula steps : 17
% 0.35/23.54 # Proof object conjectures : 6
% 0.35/23.54 # Proof object clause conjectures : 3
% 0.35/23.54 # Proof object formula conjectures : 3
% 0.35/23.54 # Proof object initial clauses used : 13
% 0.35/23.54 # Proof object initial formulas used : 9
% 0.35/23.54 # Proof object generating inferences : 7
% 0.35/23.54 # Proof object simplifying inferences : 17
% 0.35/23.54 # Training examples: 0 positive, 0 negative
% 0.35/23.54 # Parsed axioms : 49
% 0.35/23.54 # Removed by relevancy pruning/SinE : 1
% 0.35/23.54 # Initial clauses : 234
% 0.35/23.54 # Removed in clause preprocessing : 3
% 0.35/23.54 # Initial clauses in saturation : 231
% 0.35/23.54 # Processed clauses : 361
% 0.35/23.54 # ...of these trivial : 12
% 0.35/23.54 # ...subsumed : 68
% 0.35/23.54 # ...remaining for further processing : 281
% 0.35/23.54 # Other redundant clauses eliminated : 31
% 0.35/23.54 # Clauses deleted for lack of memory : 0
% 0.35/23.54 # Backward-subsumed : 1
% 0.35/23.54 # Backward-rewritten : 4
% 0.35/23.54 # Generated clauses : 3721
% 0.35/23.54 # ...of the previous two non-trivial : 3579
% 0.35/23.54 # Contextual simplify-reflections : 8
% 0.35/23.54 # Paramodulations : 3670
% 0.35/23.54 # Factorizations : 0
% 0.35/23.54 # Equation resolutions : 51
% 0.35/23.54 # Current number of processed clauses : 275
% 0.35/23.54 # Positive orientable unit clauses : 45
% 0.35/23.54 # Positive unorientable unit clauses: 0
% 0.35/23.54 # Negative unit clauses : 12
% 0.35/23.54 # Non-unit-clauses : 218
% 0.35/23.54 # Current number of unprocessed clauses: 3409
% 0.35/23.54 # ...number of literals in the above : 33539
% 0.35/23.54 # Current number of archived formulas : 0
% 0.35/23.54 # Current number of archived clauses : 5
% 0.35/23.54 # Clause-clause subsumption calls (NU) : 25087
% 0.35/23.54 # Rec. Clause-clause subsumption calls : 972
% 0.35/23.54 # Non-unit clause-clause subsumptions : 56
% 0.35/23.54 # Unit Clause-clause subsumption calls : 2084
% 0.35/23.54 # Rewrite failures with RHS unbound : 0
% 0.35/23.54 # BW rewrite match attempts : 2
% 0.35/23.54 # BW rewrite match successes : 2
% 0.35/23.54 # Condensation attempts : 0
% 0.35/23.54 # Condensation successes : 0
% 0.35/23.54 # Termbank termtop insertions : 139044
% 0.35/23.54
% 0.35/23.54 # -------------------------------------------------
% 0.35/23.54 # User time : 0.095 s
% 0.35/23.54 # System time : 0.006 s
% 0.35/23.54 # Total time : 0.101 s
% 0.35/23.54 # Maximum resident set size: 7392 pages
%------------------------------------------------------------------------------