TSTP Solution File: NUM505+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n008.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 09:33:10 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 141 ( 43 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 172 ( 66 ~; 72 |; 24 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 19 !; 0 ?)
% 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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefQuot) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefPrime) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1837) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETotal) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).
fof(m__,conjecture,
( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(c_0_8,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| X5 != sdtasdt0(X4,X6)
| X6 = sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(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)],[mDefQuot])])])])])]) ).
fof(c_0_9,plain,
! [X3,X4] :
( ( X3 != sz00
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( X3 != sz10
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| X4 = sz10
| X4 = X3
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk3_1(X3))
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk3_1(X3),X3)
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != sz10
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != X3
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
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)],[mDefPrime])])])])])])]) ).
cnf(c_0_10,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_14,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_15,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_17,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_18,hypothesis,
sz00 != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
fof(c_0_19,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_20,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_21,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
( aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_13])]),c_0_18]) ).
cnf(c_0_23,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_26,negated_conjecture,
( ~ sdtlseqdt0(xp,xk)
& ( xk = xp
| ~ sdtlseqdt0(xk,xp) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_20])]) ).
cnf(c_0_27,hypothesis,
( sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(xk,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
xp = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_33,hypothesis,
sdtlseqdt0(xk,xk),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n008.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 12:28:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.019 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 35
% 0.23/1.42 # Proof object clause steps : 21
% 0.23/1.42 # Proof object formula steps : 14
% 0.23/1.42 # Proof object conjectures : 7
% 0.23/1.42 # Proof object clause conjectures : 4
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 12
% 0.23/1.42 # Proof object initial formulas used : 8
% 0.23/1.42 # Proof object generating inferences : 6
% 0.23/1.42 # Proof object simplifying inferences : 16
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 50
% 0.23/1.42 # Removed by relevancy pruning/SinE : 1
% 0.23/1.42 # Initial clauses : 91
% 0.23/1.42 # Removed in clause preprocessing : 3
% 0.23/1.42 # Initial clauses in saturation : 88
% 0.23/1.42 # Processed clauses : 395
% 0.23/1.42 # ...of these trivial : 4
% 0.23/1.42 # ...subsumed : 150
% 0.23/1.42 # ...remaining for further processing : 240
% 0.23/1.42 # Other redundant clauses eliminated : 20
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 8
% 0.23/1.42 # Backward-rewritten : 83
% 0.23/1.42 # Generated clauses : 1158
% 0.23/1.42 # ...of the previous two non-trivial : 1077
% 0.23/1.42 # Contextual simplify-reflections : 63
% 0.23/1.42 # Paramodulations : 1122
% 0.23/1.42 # Factorizations : 2
% 0.23/1.42 # Equation resolutions : 34
% 0.23/1.42 # Current number of processed clauses : 148
% 0.23/1.42 # Positive orientable unit clauses : 22
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 6
% 0.23/1.42 # Non-unit-clauses : 120
% 0.23/1.42 # Current number of unprocessed clauses: 579
% 0.23/1.42 # ...number of literals in the above : 3195
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 91
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 7697
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 2726
% 0.23/1.42 # Non-unit clause-clause subsumptions : 187
% 0.23/1.42 # Unit Clause-clause subsumption calls : 811
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 8
% 0.23/1.42 # BW rewrite match successes : 8
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 23908
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.055 s
% 0.23/1.42 # System time : 0.004 s
% 0.23/1.42 # Total time : 0.059 s
% 0.23/1.42 # Maximum resident set size: 4224 pages
%------------------------------------------------------------------------------