TSTP Solution File: NUM708^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------