TSTP Solution File: SET574^20 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET574^20 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 09:18:59 EDT 2024

% Result   : Theorem 0.16s 0.43s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   42 (  19 unt;  15 typ;   0 def)
%            Number of atoms       :   98 (  12 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  264 (  24   ~;  21   |;  15   &; 191   @)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   57 (  57   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   5 con; 0-3 aty)
%            Number of variables   :   51 (  34   ^  14   !;   3   ?;  51   :)

% 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_34,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(decl_35,type,
    intersect: $i > $i > mworld > $o ).

thf(decl_36,type,
    member: $i > $i > mworld > $o ).

thf(decl_38,type,
    esk2_2: $i > $i > $i ).

thf(decl_39,type,
    esk3_0: $i ).

thf(decl_40,type,
    esk4_0: $i ).

thf(decl_41,type,
    esk5_0: $i ).

thf(mlocal_def,axiom,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mlocal_def) ).

thf(mand_def,axiom,
    ( mand
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
          & ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mand_def) ).

thf(mequiv_def,axiom,
    ( mequiv
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
        <=> ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mequiv_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/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mforall_di_def) ).

thf(mexists_di_def,axiom,
    ( mexists_di
    = ( ^ [X8: $i > mworld > $o,X3: mworld] :
        ? [X6: $i] :
          ( ( eiw_di @ X6 @ X3 )
          & ( X8 @ X6 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mexists_di_def) ).

thf(mimplies_def,axiom,
    ( mimplies
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
         => ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',mimplies_def) ).

thf(intersect_defn,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [X9: $i] :
          ( mforall_di
          @ ^ [X10: $i] :
              ( mequiv @ ( intersect @ X9 @ X10 )
              @ ( mexists_di
                @ ^ [X11: $i] : ( mand @ ( member @ X11 @ X9 ) @ ( member @ X11 @ X10 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',intersect_defn) ).

thf(prove_th13,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [X13: $i] :
          ( mforall_di
          @ ^ [X10: $i] :
              ( mforall_di
              @ ^ [X11: $i] : ( mimplies @ ( mand @ ( member @ X13 @ X10 ) @ ( member @ X13 @ X11 ) ) @ ( intersect @ X10 @ X11 ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.vcsPQRrJtO/E---3.1_31341.p',prove_th13) ).

thf(c_0_8,plain,
    ( mlocal
    = ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
    inference(fof_simplification,[status(thm)],[mlocal_def]) ).

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

thf(c_0_10,plain,
    ( mequiv
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
        <=> ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mequiv_def]) ).

thf(c_0_11,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_12,plain,
    ( mexists_di
    = ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
        ? [X6: $i] :
          ( ( eiw_di @ X6 @ Z1 )
          & ( Z0 @ X6 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mexists_di_def]) ).

thf(c_0_13,plain,
    ( mimplies
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
         => ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies_def]) ).

thf(c_0_14,plain,
    ! [X22: $i] :
      ( ( eiw_di @ X22 @ mactual )
     => ! [X21: $i] :
          ( ( eiw_di @ X21 @ mactual )
         => ( ( intersect @ X22 @ X21 @ mactual )
          <=> ? [X20: $i] :
                ( ( eiw_di @ X20 @ mactual )
                & ( member @ X20 @ X22 @ mactual )
                & ( member @ X20 @ X21 @ mactual ) ) ) ) ),
    inference(apply_def,[status(thm)],[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)],[intersect_defn]),c_0_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]) ).

thf(c_0_15,negated_conjecture,
    ~ ! [X27: $i] :
        ( ( eiw_di @ X27 @ mactual )
       => ! [X26: $i] :
            ( ( eiw_di @ X26 @ mactual )
           => ! [X25: $i] :
                ( ( eiw_di @ X25 @ mactual )
               => ( ( ( member @ X27 @ X26 @ mactual )
                    & ( member @ X27 @ X25 @ mactual ) )
                 => ( intersect @ X26 @ X25 @ 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)],[prove_th13])]),c_0_8]),c_0_9]),c_0_13]),c_0_11]) ).

thf(c_0_16,plain,
    ! [X34: $i,X35: $i,X37: $i] :
      ( ( ( eiw_di @ ( esk2_2 @ X34 @ X35 ) @ mactual )
        | ~ ( intersect @ X34 @ X35 @ mactual )
        | ~ ( eiw_di @ X35 @ mactual )
        | ~ ( eiw_di @ X34 @ mactual ) )
      & ( ( member @ ( esk2_2 @ X34 @ X35 ) @ X34 @ mactual )
        | ~ ( intersect @ X34 @ X35 @ mactual )
        | ~ ( eiw_di @ X35 @ mactual )
        | ~ ( eiw_di @ X34 @ mactual ) )
      & ( ( member @ ( esk2_2 @ X34 @ X35 ) @ X35 @ mactual )
        | ~ ( intersect @ X34 @ X35 @ mactual )
        | ~ ( eiw_di @ X35 @ mactual )
        | ~ ( eiw_di @ X34 @ mactual ) )
      & ( ~ ( eiw_di @ X37 @ mactual )
        | ~ ( member @ X37 @ X34 @ mactual )
        | ~ ( member @ X37 @ X35 @ mactual )
        | ( intersect @ X34 @ X35 @ mactual )
        | ~ ( eiw_di @ X35 @ mactual )
        | ~ ( eiw_di @ X34 @ mactual ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])])]) ).

thf(c_0_17,negated_conjecture,
    ( ( eiw_di @ esk3_0 @ mactual )
    & ( eiw_di @ esk4_0 @ mactual )
    & ( eiw_di @ esk5_0 @ mactual )
    & ( member @ esk3_0 @ esk4_0 @ mactual )
    & ( member @ esk3_0 @ esk5_0 @ mactual )
    & ~ ( intersect @ esk4_0 @ esk5_0 @ mactual ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

thf(c_0_18,plain,
    ! [X6: $i,X10: $i,X9: $i] :
      ( ( intersect @ X9 @ X10 @ mactual )
      | ~ ( eiw_di @ X6 @ mactual )
      | ~ ( member @ X6 @ X9 @ mactual )
      | ~ ( member @ X6 @ X10 @ mactual )
      | ~ ( eiw_di @ X10 @ mactual )
      | ~ ( eiw_di @ X9 @ mactual ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,negated_conjecture,
    member @ esk3_0 @ esk5_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_20,negated_conjecture,
    eiw_di @ esk5_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_21,negated_conjecture,
    eiw_di @ esk3_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_22,negated_conjecture,
    ! [X6: $i] :
      ( ( intersect @ X6 @ esk5_0 @ mactual )
      | ~ ( member @ esk3_0 @ X6 @ mactual )
      | ~ ( eiw_di @ X6 @ mactual ) ),
    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])]) ).

thf(c_0_23,negated_conjecture,
    member @ esk3_0 @ esk4_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_24,negated_conjecture,
    eiw_di @ esk4_0 @ mactual,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_25,negated_conjecture,
    ~ ( intersect @ esk4_0 @ esk5_0 @ mactual ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SET574^20 : TPTP v8.1.2. Released v8.1.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 10:23:54 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.16/0.42  Running higher-order theorem proving
% 0.16/0.42  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.vcsPQRrJtO/E---3.1_31341.p
% 0.16/0.43  # Version: 3.1.0-ho
% 0.16/0.43  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.16/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.43  # Starting post_as_ho3 with 300s (1) cores
% 0.16/0.43  # Starting new_ho_12 with 300s (1) cores
% 0.16/0.43  # Starting new_bool_2 with 300s (1) cores
% 0.16/0.43  # post_as_ho3 with pid 31420 completed with status 0
% 0.16/0.43  # Result found by post_as_ho3
% 0.16/0.43  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.16/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.43  # Starting post_as_ho3 with 300s (1) cores
% 0.16/0.43  # No SInE strategy applied
% 0.16/0.43  # Search class: HHUNS-FFSS21-SHSSMFNN
% 0.16/0.43  # partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.16/0.43  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.43  # new_ho_10 with pid 31425 completed with status 0
% 0.16/0.43  # Result found by new_ho_10
% 0.16/0.43  # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.16/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.43  # Starting post_as_ho3 with 300s (1) cores
% 0.16/0.43  # No SInE strategy applied
% 0.16/0.43  # Search class: HHUNS-FFSS21-SHSSMFNN
% 0.16/0.43  # partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.16/0.43  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.43  # Preprocessing time       : 0.001 s
% 0.16/0.43  # Presaturation interreduction done
% 0.16/0.43  
% 0.16/0.43  # Proof found!
% 0.16/0.43  # SZS status Theorem
% 0.16/0.43  # SZS output start CNFRefutation
% See solution above
% 0.16/0.43  # Parsed axioms                        : 32
% 0.16/0.43  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.43  # Initial clauses                      : 30
% 0.16/0.43  # Removed in clause preprocessing      : 16
% 0.16/0.43  # Initial clauses in saturation        : 14
% 0.16/0.43  # Processed clauses                    : 29
% 0.16/0.43  # ...of these trivial                  : 0
% 0.16/0.43  # ...subsumed                          : 0
% 0.16/0.43  # ...remaining for further processing  : 29
% 0.16/0.43  # Other redundant clauses eliminated   : 0
% 0.16/0.43  # Clauses deleted for lack of memory   : 0
% 0.16/0.43  # Backward-subsumed                    : 0
% 0.16/0.43  # Backward-rewritten                   : 0
% 0.16/0.43  # Generated clauses                    : 7
% 0.16/0.43  # ...of the previous two non-redundant : 5
% 0.16/0.43  # ...aggressively subsumed             : 0
% 0.16/0.43  # Contextual simplify-reflections      : 0
% 0.16/0.43  # Paramodulations                      : 7
% 0.16/0.43  # Factorizations                       : 0
% 0.16/0.43  # NegExts                              : 0
% 0.16/0.43  # Equation resolutions                 : 0
% 0.16/0.43  # Disequality decompositions           : 0
% 0.16/0.43  # Total rewrite steps                  : 6
% 0.16/0.43  # ...of those cached                   : 3
% 0.16/0.43  # Propositional unsat checks           : 0
% 0.16/0.43  #    Propositional check models        : 0
% 0.16/0.43  #    Propositional check unsatisfiable : 0
% 0.16/0.43  #    Propositional clauses             : 0
% 0.16/0.43  #    Propositional clauses after purity: 0
% 0.16/0.43  #    Propositional unsat core size     : 0
% 0.16/0.43  #    Propositional preprocessing time  : 0.000
% 0.16/0.43  #    Propositional encoding time       : 0.000
% 0.16/0.43  #    Propositional solver time         : 0.000
% 0.16/0.43  #    Success case prop preproc time    : 0.000
% 0.16/0.43  #    Success case prop encoding time   : 0.000
% 0.16/0.43  #    Success case prop solver time     : 0.000
% 0.16/0.43  # Current number of processed clauses  : 15
% 0.16/0.43  #    Positive orientable unit clauses  : 7
% 0.16/0.43  #    Positive unorientable unit clauses: 0
% 0.16/0.43  #    Negative unit clauses             : 1
% 0.16/0.43  #    Non-unit-clauses                  : 7
% 0.16/0.43  # Current number of unprocessed clauses: 3
% 0.16/0.43  # ...number of literals in the above   : 17
% 0.16/0.43  # Current number of archived formulas  : 0
% 0.16/0.43  # Current number of archived clauses   : 14
% 0.16/0.43  # Clause-clause subsumption calls (NU) : 32
% 0.16/0.43  # Rec. Clause-clause subsumption calls : 0
% 0.16/0.43  # Non-unit clause-clause subsumptions  : 0
% 0.16/0.43  # Unit Clause-clause subsumption calls : 0
% 0.16/0.43  # Rewrite failures with RHS unbound    : 0
% 0.16/0.43  # BW rewrite match attempts            : 0
% 0.16/0.43  # BW rewrite match successes           : 0
% 0.16/0.43  # Condensation attempts                : 29
% 0.16/0.43  # Condensation successes               : 0
% 0.16/0.43  # Termbank termtop insertions          : 2478
% 0.16/0.43  # Search garbage collected termcells   : 668
% 0.16/0.43  
% 0.16/0.43  # -------------------------------------------------
% 0.16/0.43  # User time                : 0.003 s
% 0.16/0.43  # System time              : 0.003 s
% 0.16/0.43  # Total time               : 0.006 s
% 0.16/0.43  # Maximum resident set size: 1896 pages
% 0.16/0.43  
% 0.16/0.43  # -------------------------------------------------
% 0.16/0.43  # User time                : 0.003 s
% 0.16/0.43  # System time              : 0.006 s
% 0.16/0.43  # Total time               : 0.009 s
% 0.16/0.43  # Maximum resident set size: 1752 pages
% 0.16/0.43  % E---3.1 exiting
% 0.16/0.43  % E exiting
%------------------------------------------------------------------------------