TSTP Solution File: NUM708^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM708^4 : TPTP v8.2.0. Released v7.1.0.
% 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 : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:15:46 EDT 2024
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% 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/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(satz28g,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ X1 @ ( n_ts @ n_1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz28g) ).
thf(satz28c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_ts @ n_1 @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz28c) ).
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,
~ ! [X445: $i] :
( ( in @ X445 @ nat )
=> ( X445
= ( n_ts @ n_1 @ X445 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz28g])]),c_0_9]),c_0_10]) ).
thf(c_0_12,plain,
! [X469: $i] :
( ( in @ X469 @ nat )
=> ( ( n_ts @ n_1 @ X469 )
= X469 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz28c]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( esk1_0
!= ( n_ts @ n_1 @ esk1_0 ) ) ),
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,
! [X631: $i] :
( ~ ( in @ X631 @ nat )
| ( ( n_ts @ n_1 @ X631 )
= X631 ) ),
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 @ n_1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( ( n_ts @ n_1 @ X1 )
= 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
% 0.04/0.12 % Problem : NUM708^4 : TPTP v8.2.0. Released v7.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 20 04:32:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 # Version: 3.1.0-ho
% 0.19/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.19/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.19/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.19/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.19/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.19/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.19/0.53 # Starting ho_unfolding_6 with 300s (1) cores
% 0.19/0.53 # pre_casc_4 with pid 31257 completed with status 0
% 0.19/0.53 # Result found by pre_casc_4
% 0.19/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.19/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.19/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.19/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.19/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.19/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.19/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.53 # Search class: HGUSM-FSLM31-DHSMMSBN
% 0.19/0.53 # partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.19/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.19/0.53 # new_ho_10_cnf2 with pid 31259 completed with status 0
% 0.19/0.53 # Result found by new_ho_10_cnf2
% 0.19/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.19/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.19/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.19/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.19/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.19/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.19/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.53 # Search class: HGUSM-FSLM31-DHSMMSBN
% 0.19/0.53 # partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.19/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.19/0.53 # Preprocessing time : 0.004 s
% 0.19/0.53 # Presaturation interreduction done
% 0.19/0.53
% 0.19/0.53 # Proof found!
% 0.19/0.53 # SZS status Theorem
% 0.19/0.53 # SZS output start CNFRefutation
% See solution above
% 0.19/0.54 # Parsed axioms : 438
% 0.19/0.54 # Removed by relevancy pruning/SinE : 325
% 0.19/0.54 # Initial clauses : 154
% 0.19/0.54 # Removed in clause preprocessing : 9
% 0.19/0.54 # Initial clauses in saturation : 145
% 0.19/0.54 # Processed clauses : 161
% 0.19/0.54 # ...of these trivial : 4
% 0.19/0.54 # ...subsumed : 23
% 0.19/0.54 # ...remaining for further processing : 134
% 0.19/0.54 # Other redundant clauses eliminated : 7
% 0.19/0.54 # Clauses deleted for lack of memory : 0
% 0.19/0.54 # Backward-subsumed : 0
% 0.19/0.54 # Backward-rewritten : 0
% 0.19/0.54 # Generated clauses : 9
% 0.19/0.54 # ...of the previous two non-redundant : 8
% 0.19/0.54 # ...aggressively subsumed : 0
% 0.19/0.54 # Contextual simplify-reflections : 0
% 0.19/0.54 # Paramodulations : 2
% 0.19/0.54 # Factorizations : 0
% 0.19/0.54 # NegExts : 0
% 0.19/0.54 # Equation resolutions : 7
% 0.19/0.54 # Disequality decompositions : 0
% 0.19/0.54 # Total rewrite steps : 15
% 0.19/0.54 # ...of those cached : 5
% 0.19/0.54 # Propositional unsat checks : 0
% 0.19/0.54 # Propositional check models : 0
% 0.19/0.54 # Propositional check unsatisfiable : 0
% 0.19/0.54 # Propositional clauses : 0
% 0.19/0.54 # Propositional clauses after purity: 0
% 0.19/0.54 # Propositional unsat core size : 0
% 0.19/0.54 # Propositional preprocessing time : 0.000
% 0.19/0.54 # Propositional encoding time : 0.000
% 0.19/0.54 # Propositional solver time : 0.000
% 0.19/0.54 # Success case prop preproc time : 0.000
% 0.19/0.54 # Success case prop encoding time : 0.000
% 0.19/0.54 # Success case prop solver time : 0.000
% 0.19/0.54 # Current number of processed clauses : 9
% 0.19/0.54 # Positive orientable unit clauses : 4
% 0.19/0.54 # Positive unorientable unit clauses: 0
% 0.19/0.54 # Negative unit clauses : 3
% 0.19/0.54 # Non-unit-clauses : 2
% 0.19/0.54 # Current number of unprocessed clauses: 110
% 0.19/0.54 # ...number of literals in the above : 346
% 0.19/0.54 # Current number of archived formulas : 0
% 0.19/0.54 # Current number of archived clauses : 118
% 0.19/0.54 # Clause-clause subsumption calls (NU) : 3041
% 0.19/0.54 # Rec. Clause-clause subsumption calls : 644
% 0.19/0.54 # Non-unit clause-clause subsumptions : 23
% 0.19/0.54 # Unit Clause-clause subsumption calls : 11
% 0.19/0.54 # Rewrite failures with RHS unbound : 0
% 0.19/0.54 # BW rewrite match attempts : 1
% 0.19/0.54 # BW rewrite match successes : 0
% 0.19/0.54 # Condensation attempts : 161
% 0.19/0.54 # Condensation successes : 0
% 0.19/0.54 # Termbank termtop insertions : 33195
% 0.19/0.54 # Search garbage collected termcells : 10942
% 0.19/0.54
% 0.19/0.54 # -------------------------------------------------
% 0.19/0.54 # User time : 0.033 s
% 0.19/0.54 # System time : 0.006 s
% 0.19/0.54 # Total time : 0.039 s
% 0.19/0.54 # Maximum resident set size: 4064 pages
% 0.19/0.54
% 0.19/0.54 # -------------------------------------------------
% 0.19/0.54 # User time : 0.044 s
% 0.19/0.54 # System time : 0.009 s
% 0.19/0.54 # Total time : 0.054 s
% 0.19/0.54 # Maximum resident set size: 2460 pages
% 0.19/0.54 % E---3.1 exiting
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------