TSTP Solution File: NUM498+3 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM498+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:56:03 EDT 2023
% Result : Theorem 0.64s 0.59s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 144 ( 81 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 148 ( 49 ~; 46 |; 46 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 30 ( 0 sgn; 13 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m_MulZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',mZeroMul) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',mSortsC) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__1837) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__2306) ).
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/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__1860) ).
fof(m__2287,hypothesis,
( xn != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__2287) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m_MulUnit) ).
fof(c_0_9,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,negated_conjecture,
! [X21,X22] :
( ( xk = sz00
| xk = sz10 )
& ( ~ aNaturalNumber0(X21)
| xn != sdtasdt0(xp,X21) )
& ~ doDivides0(xp,xn)
& ( ~ aNaturalNumber0(X22)
| xm != sdtasdt0(xp,X22) )
& ~ doDivides0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_11,plain,
! [X45] :
( ( sdtasdt0(X45,sz00) = sz00
| ~ aNaturalNumber0(X45) )
& ( sz00 = sdtasdt0(sz00,X45)
| ~ aNaturalNumber0(X45) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_12,plain,
! [X52,X53] :
( ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| sdtasdt0(X52,X53) != sz00
| X52 = sz00
| X53 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_13,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_17,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_22,negated_conjecture,
xm != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_23,negated_conjecture,
xn != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).
fof(c_0_24,hypothesis,
! [X14,X15] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X15)
| xp != sdtasdt0(X14,X15)
| ~ aNaturalNumber0(X14)
| X14 = sz10
| X14 = xp )
& ( ~ doDivides0(X14,xp)
| ~ aNaturalNumber0(X14)
| X14 = sz10
| X14 = 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_25,hypothesis,
( xn != xp
& aNaturalNumber0(esk6_0)
& sdtpldt0(xn,esk6_0) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(esk7_0)
& sdtpldt0(xm,esk7_0) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2287])]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(sr,[status(thm)],[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]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( xk = sz00
| xk = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,hypothesis,
( X2 = sz10
| X2 = xp
| ~ aNaturalNumber0(X1)
| xp != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( xk = sz10
| sdtasdt0(xp,sz00) != sz00 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( xn = sz10
| sdtasdt0(xp,xk) != xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_21]),c_0_20])]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
xk = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_16])]) ).
fof(c_0_33,plain,
! [X86] :
( ( sdtasdt0(X86,sz10) = X86
| ~ aNaturalNumber0(X86) )
& ( X86 = sdtasdt0(sz10,X86)
| ~ aNaturalNumber0(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_34,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,hypothesis,
( xn = sz10
| sdtasdt0(xp,sz10) != xp ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xp,esk5_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,hypothesis,
xn = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xp,xk) != xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_37]),c_0_38])]) ).
cnf(c_0_41,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,hypothesis,
sdtasdt0(sz10,xm) = sdtasdt0(xp,sz10),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_32]),c_0_39]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xp,sz10) != xm,
inference(rw,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_44,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : NUM498+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n027.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 2400
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Oct 2 13:54:00 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 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/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p
% 0.64/0.59 # Version: 3.1pre001
% 0.64/0.59 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59 # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59 # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59 # Starting sh5l with 300s (1) cores
% 0.64/0.59 # new_bool_1 with pid 29717 completed with status 0
% 0.64/0.59 # Result found by new_bool_1
% 0.64/0.59 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59 # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59 # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.59 # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.64/0.59 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.59 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.64/0.59 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 29719 completed with status 0
% 0.64/0.59 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.64/0.59 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59 # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59 # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.59 # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.64/0.59 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.59 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.64/0.59 # Preprocessing time : 0.004 s
% 0.64/0.59 # Presaturation interreduction done
% 0.64/0.59
% 0.64/0.59 # Proof found!
% 0.64/0.59 # SZS status Theorem
% 0.64/0.59 # SZS output start CNFRefutation
% See solution above
% 0.64/0.59 # Parsed axioms : 46
% 0.64/0.59 # Removed by relevancy pruning/SinE : 1
% 0.64/0.59 # Initial clauses : 224
% 0.64/0.59 # Removed in clause preprocessing : 3
% 0.64/0.59 # Initial clauses in saturation : 221
% 0.64/0.59 # Processed clauses : 335
% 0.64/0.59 # ...of these trivial : 1
% 0.64/0.59 # ...subsumed : 27
% 0.64/0.59 # ...remaining for further processing : 307
% 0.64/0.59 # Other redundant clauses eliminated : 8
% 0.64/0.59 # Clauses deleted for lack of memory : 0
% 0.64/0.59 # Backward-subsumed : 0
% 0.64/0.59 # Backward-rewritten : 30
% 0.64/0.59 # Generated clauses : 74
% 0.64/0.59 # ...of the previous two non-redundant : 72
% 0.64/0.59 # ...aggressively subsumed : 0
% 0.64/0.59 # Contextual simplify-reflections : 4
% 0.64/0.59 # Paramodulations : 65
% 0.64/0.59 # Factorizations : 1
% 0.64/0.59 # NegExts : 0
% 0.64/0.59 # Equation resolutions : 8
% 0.64/0.59 # Total rewrite steps : 128
% 0.64/0.59 # Propositional unsat checks : 0
% 0.64/0.59 # Propositional check models : 0
% 0.64/0.59 # Propositional check unsatisfiable : 0
% 0.64/0.59 # Propositional clauses : 0
% 0.64/0.59 # Propositional clauses after purity: 0
% 0.64/0.59 # Propositional unsat core size : 0
% 0.64/0.59 # Propositional preprocessing time : 0.000
% 0.64/0.59 # Propositional encoding time : 0.000
% 0.64/0.59 # Propositional solver time : 0.000
% 0.64/0.59 # Success case prop preproc time : 0.000
% 0.64/0.59 # Success case prop encoding time : 0.000
% 0.64/0.59 # Success case prop solver time : 0.000
% 0.64/0.59 # Current number of processed clauses : 53
% 0.64/0.59 # Positive orientable unit clauses : 17
% 0.64/0.59 # Positive unorientable unit clauses: 0
% 0.64/0.59 # Negative unit clauses : 13
% 0.64/0.59 # Non-unit-clauses : 23
% 0.64/0.59 # Current number of unprocessed clauses: 173
% 0.64/0.59 # ...number of literals in the above : 1478
% 0.64/0.59 # Current number of archived formulas : 0
% 0.64/0.59 # Current number of archived clauses : 246
% 0.64/0.59 # Clause-clause subsumption calls (NU) : 25930
% 0.64/0.59 # Rec. Clause-clause subsumption calls : 172
% 0.64/0.59 # Non-unit clause-clause subsumptions : 9
% 0.64/0.59 # Unit Clause-clause subsumption calls : 140
% 0.64/0.59 # Rewrite failures with RHS unbound : 0
% 0.64/0.59 # BW rewrite match attempts : 2
% 0.64/0.59 # BW rewrite match successes : 2
% 0.64/0.59 # Condensation attempts : 0
% 0.64/0.59 # Condensation successes : 0
% 0.64/0.59 # Termbank termtop insertions : 20499
% 0.64/0.59
% 0.64/0.59 # -------------------------------------------------
% 0.64/0.59 # User time : 0.051 s
% 0.64/0.59 # System time : 0.005 s
% 0.64/0.59 # Total time : 0.056 s
% 0.64/0.59 # Maximum resident set size: 2296 pages
% 0.64/0.59
% 0.64/0.59 # -------------------------------------------------
% 0.64/0.59 # User time : 0.052 s
% 0.64/0.59 # System time : 0.008 s
% 0.64/0.59 # Total time : 0.060 s
% 0.64/0.59 # Maximum resident set size: 1740 pages
% 0.64/0.59 % E---3.1 exiting
% 0.64/0.59 % E---3.1 exiting
%------------------------------------------------------------------------------