TSTP Solution File: SET611^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET611^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 02:54:54 EDT 2024

% Result   : Theorem 0.18s 0.47s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   33 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :  151 (   8 equ;   0 cnn)
%            Maximal formula atoms :   84 (   5 avg)
%            Number of connectives :  317 (  70   ~;  96   |;  23   &; 124   @)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   27 (  14   ^  13   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_24,type,
    emptyset: $i > $o ).

thf(decl_29,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_30,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_36,type,
    epred1_0: $i > $o ).

thf(decl_37,type,
    epred2_0: $i > $o ).

thf(decl_38,type,
    esk1_0: $i ).

thf(decl_39,type,
    esk2_0: $i ).

thf(emptyset,axiom,
    ( emptyset
    = ( ^ [X1: $i] : ~ $true ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',emptyset) ).

thf(intersection,axiom,
    ( intersection
    = ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
          ( ( X9 @ X4 )
          & ( X10 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).

thf(setminus,axiom,
    ( setminus
    = ( ^ [X11: $i > $o,X12: $i > $o,X4: $i] :
          ( ( X11 @ X4 )
          & ~ ( X12 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',setminus) ).

thf(thm,conjecture,
    ! [X22: $i > $o,X23: $i > $o] :
      ( ( ( intersection @ X22 @ X23 )
        = emptyset )
    <=> ( ( setminus @ X22 @ X23 )
        = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(c_0_4,plain,
    ( emptyset
    = ( ^ [Z0: $i] : ~ $true ) ),
    inference(fof_simplification,[status(thm)],[emptyset]) ).

thf(c_0_5,plain,
    ( intersection
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[intersection]) ).

thf(c_0_6,plain,
    ( setminus
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ~ ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setminus]) ).

thf(c_0_7,negated_conjecture,
    ~ ! [X22: $i > $o,X23: $i > $o] :
        ( ! [X26: $i] :
            ( ( ( X22 @ X26 )
              & ( X23 @ X26 ) )
          <=> ~ $true )
      <=> ! [X27: $i] :
            ( ( ( X22 @ X27 )
              & ~ ( X23 @ X27 ) )
          <=> ( X22 @ X27 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_4]),c_0_5]),c_0_6])]) ).

thf(c_0_8,negated_conjecture,
    ! [X32: $i,X33: $i] :
      ( ( ~ ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk1_0 )
        | ~ ( epred2_0 @ esk1_0 )
        | $true )
      & ( ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk1_0 )
        | ~ ( epred2_0 @ esk1_0 )
        | $true )
      & ( ~ ( epred2_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk1_0 )
        | ~ ( epred2_0 @ esk1_0 )
        | $true )
      & ( ~ ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk1_0 )
        | ~ $true )
      & ( ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk1_0 )
        | ~ $true )
      & ( ~ ( epred2_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk1_0 )
        | ~ $true )
      & ( ~ ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk2_0 )
        | ~ ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk1_0 )
        | ~ $true )
      & ( ( epred1_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk1_0 )
        | ~ $true )
      & ( ~ ( epred2_0 @ esk2_0 )
        | ( epred1_0 @ esk2_0 )
        | ( epred2_0 @ esk1_0 )
        | ~ $true )
      & ( ~ ( epred1_0 @ X33 )
        | ( epred2_0 @ X33 )
        | ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X32 )
        | ~ ( epred2_0 @ X32 )
        | ~ $true )
      & ( ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X32 )
        | ~ ( epred2_0 @ X32 )
        | ~ $true )
      & ( ~ ( epred2_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X32 )
        | ~ ( epred2_0 @ X32 )
        | ~ $true )
      & ( ~ ( epred1_0 @ X33 )
        | ( epred2_0 @ X33 )
        | ( epred1_0 @ X33 )
        | ( epred1_0 @ X32 )
        | $true )
      & ( ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ( epred1_0 @ X32 )
        | $true )
      & ( ~ ( epred2_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ( epred1_0 @ X32 )
        | $true )
      & ( ~ ( epred1_0 @ X33 )
        | ( epred2_0 @ X33 )
        | ( epred1_0 @ X33 )
        | ( epred2_0 @ X32 )
        | $true )
      & ( ( epred1_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ( epred2_0 @ X32 )
        | $true )
      & ( ~ ( epred2_0 @ X33 )
        | ~ ( epred1_0 @ X33 )
        | ( epred2_0 @ X32 )
        | $true ) ),
    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_7])])])])])]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ~ ( epred2_0 @ X1 )
      | ~ ( epred1_0 @ X1 )
      | ~ ( epred1_0 @ X3 )
      | ~ ( epred2_0 @ X3 )
      | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ( ( epred2_0 @ esk2_0 )
    | ( epred1_0 @ esk1_0 )
    | ~ ( epred1_0 @ esk2_0 )
    | ~ ( epred1_0 @ esk2_0 )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ( ( epred1_0 @ esk2_0 )
    | ( epred1_0 @ esk2_0 )
    | ( epred1_0 @ esk1_0 )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: $i,X1: $i] :
      ( ~ ( epred1_0 @ X3 )
      | ~ ( epred1_0 @ X1 )
      | ~ ( epred2_0 @ X3 )
      | ~ ( epred2_0 @ X1 ) ),
    inference(cn,[status(thm)],[c_0_9]) ).

thf(c_0_13,negated_conjecture,
    ( ( epred1_0 @ esk2_0 )
    | ( epred1_0 @ esk2_0 )
    | ( epred2_0 @ esk1_0 )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,negated_conjecture,
    ( ( epred2_0 @ esk2_0 )
    | ( epred2_0 @ esk1_0 )
    | ~ ( epred1_0 @ esk2_0 )
    | ~ ( epred1_0 @ esk2_0 )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,negated_conjecture,
    ( ( epred1_0 @ esk1_0 )
    | ( epred2_0 @ esk2_0 )
    | ~ ( epred1_0 @ esk2_0 ) ),
    inference(cn,[status(thm)],[c_0_10]) ).

thf(c_0_16,negated_conjecture,
    ( ( epred1_0 @ esk1_0 )
    | ( epred1_0 @ esk2_0 ) ),
    inference(cn,[status(thm)],[c_0_11]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( epred1_0 @ X1 )
      | ~ ( epred2_0 @ X1 ) ),
    inference(condense,[status(thm)],[c_0_12]) ).

thf(c_0_18,negated_conjecture,
    ( ( epred1_0 @ esk2_0 )
    | ( epred2_0 @ esk1_0 ) ),
    inference(cn,[status(thm)],[c_0_13]) ).

thf(c_0_19,negated_conjecture,
    ( ( epred2_0 @ esk1_0 )
    | ( epred2_0 @ esk2_0 )
    | ~ ( epred1_0 @ esk2_0 ) ),
    inference(cn,[status(thm)],[c_0_14]) ).

thf(c_0_20,negated_conjecture,
    ( ( epred2_0 @ esk2_0 )
    | ( epred1_0 @ esk1_0 ) ),
    inference(csr,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_21,negated_conjecture,
    epred1_0 @ esk2_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).

thf(c_0_22,negated_conjecture,
    ( ( epred2_0 @ esk2_0 )
    | ( epred2_0 @ esk1_0 ) ),
    inference(csr,[status(thm)],[c_0_19,c_0_18]) ).

thf(c_0_23,negated_conjecture,
    epred1_0 @ esk1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_21])]) ).

thf(c_0_24,negated_conjecture,
    epred2_0 @ esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_23])]) ).

thf(c_0_25,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET611^3 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n004.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 11:17:22 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.18/0.46  Running higher-order theorem proving
% 0.18/0.46  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
% 0.18/0.47  # Version: 3.1.0-ho
% 0.18/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.18/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.47  # Starting sh1l with 300s (1) cores
% 0.18/0.47  # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.47  # sh1l with pid 24007 completed with status 0
% 0.18/0.47  # Result found by sh1l
% 0.18/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.18/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.47  # Starting sh1l with 300s (1) cores
% 0.18/0.47  # No SInE strategy applied
% 0.18/0.47  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.18/0.47  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.47  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.47  # new_ho_10 with pid 24012 completed with status 0
% 0.18/0.47  # Result found by new_ho_10
% 0.18/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.18/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.47  # Starting sh1l with 300s (1) cores
% 0.18/0.47  # No SInE strategy applied
% 0.18/0.47  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.18/0.47  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.47  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.47  # Preprocessing time       : 0.001 s
% 0.18/0.47  # Presaturation interreduction done
% 0.18/0.47  
% 0.18/0.47  # Proof found!
% 0.18/0.47  # SZS status Theorem
% 0.18/0.47  # SZS output start CNFRefutation
% See solution above
% 0.18/0.47  # Parsed axioms                        : 29
% 0.18/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.18/0.47  # Initial clauses                      : 32
% 0.18/0.47  # Removed in clause preprocessing      : 25
% 0.18/0.47  # Initial clauses in saturation        : 7
% 0.18/0.47  # Processed clauses                    : 15
% 0.18/0.47  # ...of these trivial                  : 0
% 0.18/0.47  # ...subsumed                          : 2
% 0.18/0.47  # ...remaining for further processing  : 13
% 0.18/0.47  # Other redundant clauses eliminated   : 0
% 0.18/0.47  # Clauses deleted for lack of memory   : 0
% 0.18/0.47  # Backward-subsumed                    : 0
% 0.18/0.47  # Backward-rewritten                   : 4
% 0.18/0.47  # Generated clauses                    : 4
% 0.18/0.47  # ...of the previous two non-redundant : 3
% 0.18/0.47  # ...aggressively subsumed             : 0
% 0.18/0.47  # Contextual simplify-reflections      : 3
% 0.18/0.47  # Paramodulations                      : 4
% 0.18/0.47  # Factorizations                       : 0
% 0.18/0.47  # NegExts                              : 0
% 0.18/0.47  # Equation resolutions                 : 0
% 0.18/0.47  # Disequality decompositions           : 0
% 0.18/0.47  # Total rewrite steps                  : 7
% 0.18/0.47  # ...of those cached                   : 4
% 0.18/0.47  # Propositional unsat checks           : 0
% 0.18/0.47  #    Propositional check models        : 0
% 0.18/0.47  #    Propositional check unsatisfiable : 0
% 0.18/0.47  #    Propositional clauses             : 0
% 0.18/0.47  #    Propositional clauses after purity: 0
% 0.18/0.47  #    Propositional unsat core size     : 0
% 0.18/0.47  #    Propositional preprocessing time  : 0.000
% 0.18/0.47  #    Propositional encoding time       : 0.000
% 0.18/0.47  #    Propositional solver time         : 0.000
% 0.18/0.47  #    Success case prop preproc time    : 0.000
% 0.18/0.47  #    Success case prop encoding time   : 0.000
% 0.18/0.47  #    Success case prop solver time     : 0.000
% 0.18/0.47  # Current number of processed clauses  : 4
% 0.18/0.47  #    Positive orientable unit clauses  : 3
% 0.18/0.47  #    Positive unorientable unit clauses: 0
% 0.18/0.47  #    Negative unit clauses             : 0
% 0.18/0.47  #    Non-unit-clauses                  : 1
% 0.18/0.47  # Current number of unprocessed clauses: 0
% 0.18/0.47  # ...number of literals in the above   : 0
% 0.18/0.47  # Current number of archived formulas  : 0
% 0.18/0.47  # Current number of archived clauses   : 9
% 0.18/0.47  # Clause-clause subsumption calls (NU) : 12
% 0.18/0.47  # Rec. Clause-clause subsumption calls : 11
% 0.18/0.47  # Non-unit clause-clause subsumptions  : 6
% 0.18/0.47  # Unit Clause-clause subsumption calls : 1
% 0.18/0.47  # Rewrite failures with RHS unbound    : 0
% 0.18/0.47  # BW rewrite match attempts            : 3
% 0.18/0.47  # BW rewrite match successes           : 3
% 0.18/0.47  # Condensation attempts                : 15
% 0.18/0.47  # Condensation successes               : 1
% 0.18/0.47  # Termbank termtop insertions          : 1738
% 0.18/0.47  # Search garbage collected termcells   : 353
% 0.18/0.47  
% 0.18/0.47  # -------------------------------------------------
% 0.18/0.47  # User time                : 0.005 s
% 0.18/0.47  # System time              : 0.000 s
% 0.18/0.47  # Total time               : 0.005 s
% 0.18/0.47  # Maximum resident set size: 1724 pages
% 0.18/0.47  
% 0.18/0.47  # -------------------------------------------------
% 0.18/0.47  # User time                : 0.008 s
% 0.18/0.47  # System time              : 0.001 s
% 0.18/0.47  # Total time               : 0.009 s
% 0.18/0.47  # Maximum resident set size: 1756 pages
% 0.18/0.47  % E---3.1 exiting
% 0.18/0.47  % E exiting
%------------------------------------------------------------------------------