TSTP Solution File: NUM706^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM706^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : Sat May 4 08:56:24 EDT 2024
% Result : Theorem 0.34s 0.56s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 28 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 42 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 5 ~; 2 |; 1 &; 49 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 24 ^ 7 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_130,type,
n_1: $i ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_164,type,
esk1_0: $i ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',def_e_is) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',def_n_is) ).
thf(satz28e,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ X1 @ ( n_ts @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',satz28e) ).
thf(satz28a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_ts @ X1 @ n_1 ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.f6D08fWOZF/E---3.1_26713.p',satz28a) ).
thf(c_0_6,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_7,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_8,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_9,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ! [X443: $i] :
( ( in @ X443 @ nat )
=> ( X443
= ( n_ts @ X443 @ n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz28e])]),c_0_9]),c_0_10]) ).
thf(c_0_12,plain,
! [X464: $i] :
( ( in @ X464 @ nat )
=> ( ( n_ts @ X464 @ n_1 )
= X464 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz28a]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( esk1_0
!= ( n_ts @ esk1_0 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
thf(c_0_14,plain,
! [X623: $i] :
( ~ ( in @ X623 @ nat )
| ( ( n_ts @ X623 @ n_1 )
= X623 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
thf(c_0_15,negated_conjecture,
( esk1_0
!= ( n_ts @ esk1_0 @ n_1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( ( n_ts @ X1 @ n_1 )
= X1 )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : NUM706^4 : TPTP v8.1.2. Released v7.1.0.
% 0.05/0.15 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 09:17:02 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.20/0.50 Running higher-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/solver/bin/eprover-ho --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.f6D08fWOZF/E---3.1_26713.p
% 0.34/0.56 # Version: 3.1.0-ho
% 0.34/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.34/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.34/0.56 # Starting almost_fo_4 with 300s (1) cores
% 0.34/0.56 # Starting new_ho_9 with 300s (1) cores
% 0.34/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.34/0.56 # Starting ho_unfolding_6 with 300s (1) cores
% 0.34/0.56 # pre_casc_4 with pid 26795 completed with status 0
% 0.34/0.56 # Result found by pre_casc_4
% 0.34/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.34/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.34/0.56 # Starting almost_fo_4 with 300s (1) cores
% 0.34/0.56 # Starting new_ho_9 with 300s (1) cores
% 0.34/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.34/0.56 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.34/0.56 # Search class: HGUSM-FSLM31-DHSMMSBN
% 0.34/0.56 # partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.34/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.56 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.34/0.56 # new_ho_10_cnf2 with pid 26797 completed with status 0
% 0.34/0.56 # Result found by new_ho_10_cnf2
% 0.34/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.34/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.34/0.56 # Starting almost_fo_4 with 300s (1) cores
% 0.34/0.56 # Starting new_ho_9 with 300s (1) cores
% 0.34/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.34/0.56 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.34/0.56 # Search class: HGUSM-FSLM31-DHSMMSBN
% 0.34/0.56 # partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.34/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.56 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.34/0.56 # Preprocessing time : 0.004 s
% 0.34/0.56 # Presaturation interreduction done
% 0.34/0.56
% 0.34/0.56 # Proof found!
% 0.34/0.56 # SZS status Theorem
% 0.34/0.56 # SZS output start CNFRefutation
% See solution above
% 0.34/0.56 # Parsed axioms : 436
% 0.34/0.56 # Removed by relevancy pruning/SinE : 325
% 0.34/0.56 # Initial clauses : 152
% 0.34/0.56 # Removed in clause preprocessing : 9
% 0.34/0.56 # Initial clauses in saturation : 143
% 0.34/0.56 # Processed clauses : 159
% 0.34/0.56 # ...of these trivial : 4
% 0.34/0.56 # ...subsumed : 21
% 0.34/0.56 # ...remaining for further processing : 134
% 0.34/0.56 # Other redundant clauses eliminated : 7
% 0.34/0.56 # Clauses deleted for lack of memory : 0
% 0.34/0.56 # Backward-subsumed : 0
% 0.34/0.56 # Backward-rewritten : 0
% 0.34/0.56 # Generated clauses : 9
% 0.34/0.56 # ...of the previous two non-redundant : 8
% 0.34/0.56 # ...aggressively subsumed : 0
% 0.34/0.56 # Contextual simplify-reflections : 0
% 0.34/0.56 # Paramodulations : 2
% 0.34/0.56 # Factorizations : 0
% 0.34/0.56 # NegExts : 0
% 0.34/0.56 # Equation resolutions : 7
% 0.34/0.56 # Disequality decompositions : 0
% 0.34/0.56 # Total rewrite steps : 15
% 0.34/0.56 # ...of those cached : 5
% 0.34/0.56 # Propositional unsat checks : 0
% 0.34/0.56 # Propositional check models : 0
% 0.34/0.56 # Propositional check unsatisfiable : 0
% 0.34/0.56 # Propositional clauses : 0
% 0.34/0.56 # Propositional clauses after purity: 0
% 0.34/0.56 # Propositional unsat core size : 0
% 0.34/0.56 # Propositional preprocessing time : 0.000
% 0.34/0.56 # Propositional encoding time : 0.000
% 0.34/0.56 # Propositional solver time : 0.000
% 0.34/0.56 # Success case prop preproc time : 0.000
% 0.34/0.56 # Success case prop encoding time : 0.000
% 0.34/0.56 # Success case prop solver time : 0.000
% 0.34/0.56 # Current number of processed clauses : 9
% 0.34/0.56 # Positive orientable unit clauses : 4
% 0.34/0.56 # Positive unorientable unit clauses: 0
% 0.34/0.56 # Negative unit clauses : 4
% 0.34/0.56 # Non-unit-clauses : 1
% 0.34/0.56 # Current number of unprocessed clauses: 110
% 0.34/0.56 # ...number of literals in the above : 347
% 0.34/0.56 # Current number of archived formulas : 0
% 0.34/0.56 # Current number of archived clauses : 118
% 0.34/0.56 # Clause-clause subsumption calls (NU) : 3029
% 0.34/0.56 # Rec. Clause-clause subsumption calls : 633
% 0.34/0.56 # Non-unit clause-clause subsumptions : 21
% 0.34/0.56 # Unit Clause-clause subsumption calls : 11
% 0.34/0.56 # Rewrite failures with RHS unbound : 0
% 0.34/0.56 # BW rewrite match attempts : 1
% 0.34/0.56 # BW rewrite match successes : 0
% 0.34/0.56 # Condensation attempts : 159
% 0.34/0.56 # Condensation successes : 0
% 0.34/0.56 # Termbank termtop insertions : 32827
% 0.34/0.56 # Search garbage collected termcells : 10807
% 0.34/0.56
% 0.34/0.56 # -------------------------------------------------
% 0.34/0.56 # User time : 0.031 s
% 0.34/0.56 # System time : 0.008 s
% 0.34/0.56 # Total time : 0.038 s
% 0.34/0.56 # Maximum resident set size: 4040 pages
% 0.34/0.56
% 0.34/0.56 # -------------------------------------------------
% 0.34/0.56 # User time : 0.041 s
% 0.34/0.56 # System time : 0.011 s
% 0.34/0.56 # Total time : 0.052 s
% 0.34/0.56 # Maximum resident set size: 2444 pages
% 0.34/0.56 % E---3.1 exiting
% 0.34/0.57 % E exiting
%------------------------------------------------------------------------------