TSTP Solution File: SET019^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 02:52:30 EDT 2024

% Result   : Theorem 0.18s 0.50s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   35 (  16 unt;  12 typ;   0 def)
%            Number of atoms       :   77 (  10 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  199 (  17   ~;  14   |;  10   &; 146   @)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   47 (  47   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :   38 (  28   ^  10   !;   0   ?;  38   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    mworld: $tType ).

thf(decl_23,type,
    mactual: mworld ).

thf(decl_24,type,
    mlocal: ( mworld > $o ) > $o ).

thf(decl_26,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(decl_28,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(decl_29,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(decl_32,type,
    eiw_di: $i > mworld > $o ).

thf(decl_33,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(decl_37,type,
    equal_set: $i > $i > mworld > $o ).

thf(decl_39,type,
    subset: $i > $i > mworld > $o ).

thf(decl_52,type,
    esk5_0: $i ).

thf(decl_53,type,
    esk6_0: $i ).

thf(mlocal_def,axiom,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).

thf(mand_def,axiom,
    ( mand
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
          & ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).

thf(mimplies_def,axiom,
    ( mimplies
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
         => ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).

thf(mforall_di_def,axiom,
    ( mforall_di
    = ( ^ [X7: $i > mworld > $o,X3: mworld] :
        ! [X6: $i] :
          ( ( eiw_di @ X6 @ X3 )
         => ( X7 @ X6 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).

thf(mequiv_def,axiom,
    ( mequiv
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
        <=> ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).

thf(thI02,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [X65: $i] :
          ( mforall_di
          @ ^ [X66: $i] : ( mimplies @ ( mand @ ( subset @ X65 @ X66 ) @ ( subset @ X66 @ X65 ) ) @ ( equal_set @ X65 @ X66 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI02) ).

thf(equal_set_0,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [X50: $i] :
          ( mforall_di
          @ ^ [X51: $i] : ( mequiv @ ( equal_set @ X50 @ X51 ) @ ( mand @ ( subset @ X50 @ X51 ) @ ( subset @ X51 @ X50 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set_0) ).

thf(c_0_7,plain,
    ( mlocal
    = ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
    inference(fof_simplification,[status(thm)],[mlocal_def]) ).

thf(c_0_8,plain,
    ( mand
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mand_def]) ).

thf(c_0_9,plain,
    ( mimplies
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
         => ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies_def]) ).

thf(c_0_10,plain,
    ( mforall_di
    = ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
        ! [X6: $i] :
          ( ( eiw_di @ X6 @ Z1 )
         => ( Z0 @ X6 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_di_def]) ).

thf(c_0_11,plain,
    ( mequiv
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
        <=> ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mequiv_def]) ).

thf(c_0_12,negated_conjecture,
    ~ ! [X158: $i] :
        ( ( eiw_di @ X158 @ mactual )
       => ! [X157: $i] :
            ( ( eiw_di @ X157 @ mactual )
           => ( ( ( subset @ X158 @ X157 @ mactual )
                & ( subset @ X157 @ X158 @ mactual ) )
             => ( equal_set @ X158 @ X157 @ mactual ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thI02])]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).

thf(c_0_13,plain,
    ! [X133: $i] :
      ( ( eiw_di @ X133 @ mactual )
     => ! [X132: $i] :
          ( ( eiw_di @ X132 @ mactual )
         => ( ( equal_set @ X133 @ X132 @ mactual )
          <=> ( ( subset @ X133 @ X132 @ mactual )
              & ( subset @ X132 @ X133 @ mactual ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[equal_set_0]),c_0_7]),c_0_8]),c_0_11]),c_0_10]) ).

thf(c_0_14,negated_conjecture,
    ( ( eiw_di @ esk5_0 @ mactual )
    & ( eiw_di @ esk6_0 @ mactual )
    & ( subset @ esk5_0 @ esk6_0 @ mactual )
    & ( subset @ esk6_0 @ esk5_0 @ mactual )
    & ~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

thf(c_0_15,plain,
    ! [X225: $i,X226: $i] :
      ( ( ( subset @ X225 @ X226 @ mactual )
        | ~ ( equal_set @ X225 @ X226 @ mactual )
        | ~ ( eiw_di @ X226 @ mactual )
        | ~ ( eiw_di @ X225 @ mactual ) )
      & ( ( subset @ X226 @ X225 @ mactual )
        | ~ ( equal_set @ X225 @ X226 @ mactual )
        | ~ ( eiw_di @ X226 @ mactual )
        | ~ ( eiw_di @ X225 @ mactual ) )
      & ( ~ ( subset @ X225 @ X226 @ mactual )
        | ~ ( subset @ X226 @ X225 @ mactual )
        | ( equal_set @ X225 @ X226 @ mactual )
        | ~ ( eiw_di @ X226 @ mactual )
        | ~ ( eiw_di @ X225 @ mactual ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).

thf(c_0_16,negated_conjecture,
    ~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_17,plain,
    ! [X9: $i,X6: $i] :
      ( ( equal_set @ X6 @ X9 @ mactual )
      | ~ ( subset @ X6 @ X9 @ mactual )
      | ~ ( subset @ X9 @ X6 @ mactual )
      | ~ ( eiw_di @ X9 @ mactual )
      | ~ ( eiw_di @ X6 @ mactual ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_18,negated_conjecture,
    subset @ esk6_0 @ esk5_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_19,negated_conjecture,
    subset @ esk5_0 @ esk6_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_20,negated_conjecture,
    eiw_di @ esk6_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_21,negated_conjecture,
    eiw_di @ esk5_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.14  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon May 20 11:23:22 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.18/0.47  Running higher-order theorem proving
% 0.18/0.47  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/benchmark/theBenchmark.p
% 0.18/0.49  # Version: 3.1.0-ho
% 0.18/0.49  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49  # Starting post_as_ho3 with 300s (1) cores
% 0.18/0.49  # Starting new_ho_12 with 300s (1) cores
% 0.18/0.49  # Starting new_bool_2 with 300s (1) cores
% 0.18/0.49  # new_ho_10_cnf2 with pid 4186 completed with status 0
% 0.18/0.49  # Result found by new_ho_10_cnf2
% 0.18/0.49  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49  # No SInE strategy applied
% 0.18/0.49  # Search class: HGHNS-FFMS21-SHSSMFNN
% 0.18/0.49  # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.18/0.49  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.49  # Starting new_ho_10 with 811s (1) cores
% 0.18/0.49  # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.18/0.49  # Starting ho_unfolding_6 with 136s (1) cores
% 0.18/0.49  # Starting sh4l with 136s (1) cores
% 0.18/0.49  # Starting ehoh_best_nonlift_rwall with 136s (1) cores
% 0.18/0.49  # ho_unfolding_6 with pid 4196 completed with status 0
% 0.18/0.49  # Result found by ho_unfolding_6
% 0.18/0.49  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.50  # No SInE strategy applied
% 0.18/0.50  # Search class: HGHNS-FFMS21-SHSSMFNN
% 0.18/0.50  # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.18/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.50  # Starting new_ho_10 with 811s (1) cores
% 0.18/0.50  # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.18/0.50  # Starting ho_unfolding_6 with 136s (1) cores
% 0.18/0.50  # Preprocessing time       : 0.002 s
% 0.18/0.50  
% 0.18/0.50  # Proof found!
% 0.18/0.50  # SZS status Theorem
% 0.18/0.50  # SZS output start CNFRefutation
% See solution above
% 0.18/0.50  # Parsed axioms                        : 73
% 0.18/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.18/0.50  # Initial clauses                      : 88
% 0.18/0.50  # Removed in clause preprocessing      : 27
% 0.18/0.50  # Initial clauses in saturation        : 61
% 0.18/0.50  # Processed clauses                    : 14
% 0.18/0.50  # ...of these trivial                  : 0
% 0.18/0.50  # ...subsumed                          : 0
% 0.18/0.50  # ...remaining for further processing  : 14
% 0.18/0.50  # Other redundant clauses eliminated   : 0
% 0.18/0.50  # Clauses deleted for lack of memory   : 0
% 0.18/0.50  # Backward-subsumed                    : 0
% 0.18/0.50  # Backward-rewritten                   : 0
% 0.18/0.50  # Generated clauses                    : 9
% 0.18/0.50  # ...of the previous two non-redundant : 6
% 0.18/0.50  # ...aggressively subsumed             : 0
% 0.18/0.50  # Contextual simplify-reflections      : 0
% 0.18/0.50  # Paramodulations                      : 9
% 0.18/0.50  # Factorizations                       : 0
% 0.18/0.50  # NegExts                              : 0
% 0.18/0.50  # Equation resolutions                 : 0
% 0.18/0.50  # Disequality decompositions           : 0
% 0.18/0.50  # Total rewrite steps                  : 4
% 0.18/0.50  # ...of those cached                   : 0
% 0.18/0.50  # Propositional unsat checks           : 0
% 0.18/0.50  #    Propositional check models        : 0
% 0.18/0.50  #    Propositional check unsatisfiable : 0
% 0.18/0.50  #    Propositional clauses             : 0
% 0.18/0.50  #    Propositional clauses after purity: 0
% 0.18/0.50  #    Propositional unsat core size     : 0
% 0.18/0.50  #    Propositional preprocessing time  : 0.000
% 0.18/0.50  #    Propositional encoding time       : 0.000
% 0.18/0.50  #    Propositional solver time         : 0.000
% 0.18/0.50  #    Success case prop preproc time    : 0.000
% 0.18/0.50  #    Success case prop encoding time   : 0.000
% 0.18/0.50  #    Success case prop solver time     : 0.000
% 0.18/0.50  # Current number of processed clauses  : 14
% 0.18/0.50  #    Positive orientable unit clauses  : 6
% 0.18/0.50  #    Positive unorientable unit clauses: 0
% 0.18/0.50  #    Negative unit clauses             : 1
% 0.18/0.50  #    Non-unit-clauses                  : 7
% 0.18/0.50  # Current number of unprocessed clauses: 53
% 0.18/0.50  # ...number of literals in the above   : 247
% 0.18/0.50  # Current number of archived formulas  : 0
% 0.18/0.50  # Current number of archived clauses   : 0
% 0.18/0.50  # Clause-clause subsumption calls (NU) : 20
% 0.18/0.50  # Rec. Clause-clause subsumption calls : 3
% 0.18/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.18/0.50  # Unit Clause-clause subsumption calls : 0
% 0.18/0.50  # Rewrite failures with RHS unbound    : 0
% 0.18/0.50  # BW rewrite match attempts            : 0
% 0.18/0.50  # BW rewrite match successes           : 0
% 0.18/0.50  # Condensation attempts                : 14
% 0.18/0.50  # Condensation successes               : 0
% 0.18/0.50  # Termbank termtop insertions          : 14561
% 0.18/0.50  # Search garbage collected termcells   : 5890
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.012 s
% 0.18/0.50  # System time              : 0.005 s
% 0.18/0.50  # Total time               : 0.017 s
% 0.18/0.50  # Maximum resident set size: 2772 pages
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.025 s
% 0.18/0.50  # System time              : 0.015 s
% 0.18/0.50  # Total time               : 0.040 s
% 0.18/0.50  # Maximum resident set size: 1832 pages
% 0.18/0.50  % E---3.1 exiting
% 0.18/0.50  % E exiting
%------------------------------------------------------------------------------