TSTP Solution File: SEU634^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 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 03:28:44 EDT 2024

% Result   : Theorem 0.21s 0.52s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   28 (   3 unt;  11 typ;   0 def)
%            Number of atoms       :   54 (   5 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  197 (  13   ~;  13   |;   7   &; 147   @)
%                                         (   3 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   41 (   0   ^  39   !;   2   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_23,type,
    emptyset: $i ).

thf(decl_24,type,
    setadjoin: $i > $i > $i ).

thf(decl_25,type,
    setunion: $i > $i ).

thf(decl_26,type,
    uniqinunit: $o ).

thf(decl_27,type,
    subset: $i > $i > $o ).

thf(decl_28,type,
    subsetI2: $o ).

thf(decl_29,type,
    setunionE2: $o ).

thf(decl_30,type,
    esk1_2: $i > $i > $i ).

thf(decl_31,type,
    esk2_2: $i > $i > $i ).

thf(decl_32,type,
    esk3_0: $i ).

thf(setunionsingleton1,conjecture,
    ( uniqinunit
   => ( subsetI2
     => ( setunionE2
       => ! [X3: $i] : ( subset @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X3: $i,X4: $i] :
        ( ! [X1: $i] :
            ( ( in @ X1 @ X3 )
           => ( in @ X1 @ X4 ) )
       => ( subset @ X3 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

thf(setunionE2,axiom,
    ( setunionE2
  <=> ! [X3: $i,X1: $i] :
        ( ( in @ X1 @ ( setunion @ X3 ) )
       => ? [X5: $i] :
            ( ( in @ X5 @ X3 )
            & ( in @ X1 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).

thf(c_0_4,negated_conjecture,
    ~ ( ! [X15: $i,X16: $i] :
          ( ( in @ X15 @ ( setadjoin @ X16 @ emptyset ) )
         => ( X15 = X16 ) )
     => ( ! [X17: $i,X18: $i] :
            ( ! [X19: $i] :
                ( ( in @ X19 @ X17 )
               => ( in @ X19 @ X18 ) )
           => ( subset @ X17 @ X18 ) )
       => ( ! [X20: $i,X21: $i] :
              ( ( in @ X21 @ ( setunion @ X20 ) )
             => ? [X22: $i] :
                  ( ( in @ X22 @ X20 )
                  & ( in @ X21 @ X22 ) ) )
         => ! [X3: $i] : ( subset @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) @ X3 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setunionsingleton1]),uniqinunit]),subsetI2]),setunionE2]) ).

thf(c_0_5,negated_conjecture,
    ! [X23: $i,X24: $i,X25: $i,X26: $i,X28: $i,X29: $i] :
      ( ( ~ ( in @ X23 @ ( setadjoin @ X24 @ emptyset ) )
        | ( X23 = X24 ) )
      & ( ( in @ ( esk1_2 @ X25 @ X26 ) @ X25 )
        | ( subset @ X25 @ X26 ) )
      & ( ~ ( in @ ( esk1_2 @ X25 @ X26 ) @ X26 )
        | ( subset @ X25 @ X26 ) )
      & ( ( in @ ( esk2_2 @ X28 @ X29 ) @ X28 )
        | ~ ( in @ X29 @ ( setunion @ X28 ) ) )
      & ( ( in @ X29 @ ( esk2_2 @ X28 @ X29 ) )
        | ~ ( in @ X29 @ ( setunion @ X28 ) ) )
      & ~ ( subset @ ( setunion @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk3_0 ) ),
    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_4])])])])])]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_7,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( in @ ( esk2_2 @ X1 @ X2 ) @ X1 )
      | ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ ( esk2_2 @ X2 @ X1 ) )
      | ~ ( in @ X1 @ ( setunion @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( esk2_2 @ ( setadjoin @ X1 @ emptyset ) @ X2 )
        = X1 )
      | ~ ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ X2 )
      | ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
      | ( subset @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
      | ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( esk1_2 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) @ X1 )
      | ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ~ ( subset @ ( setunion @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem    : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.15  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n004.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 15:27:38 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.21/0.50  Running higher-order theorem proving
% 0.21/0.50  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
% 0.21/0.52  # Version: 3.1.0-ho
% 0.21/0.52  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.52  # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.52  # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52  # Starting post_as_ho2 with 300s (1) cores
% 0.21/0.52  # lpo6_lambda_fix with pid 4745 completed with status 0
% 0.21/0.52  # Result found by lpo6_lambda_fix
% 0.21/0.52  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: HGUSF-FFSF21-SFFFMFNN
% 0.21/0.52  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.52  # Starting new_ho_10 with 811s (1) cores
% 0.21/0.52  # Starting lpo6_lambda_fix with 151s (1) cores
% 0.21/0.52  # Starting new_bool_1 with 136s (1) cores
% 0.21/0.52  # Starting new_bool_2 with 136s (1) cores
% 0.21/0.52  # Starting new_bool_9 with 136s (1) cores
% 0.21/0.52  # new_ho_10 with pid 4750 completed with status 0
% 0.21/0.52  # Result found by new_ho_10
% 0.21/0.52  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: HGUSF-FFSF21-SFFFMFNN
% 0.21/0.52  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.52  # Starting new_ho_10 with 811s (1) cores
% 0.21/0.52  # Preprocessing time       : 0.001 s
% 0.21/0.52  # Presaturation interreduction done
% 0.21/0.52  
% 0.21/0.52  # Proof found!
% 0.21/0.52  # SZS status Theorem
% 0.21/0.52  # SZS output start CNFRefutation
% See solution above
% 0.21/0.52  # Parsed axioms                        : 12
% 0.21/0.52  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.52  # Initial clauses                      : 14
% 0.21/0.52  # Removed in clause preprocessing      : 8
% 0.21/0.52  # Initial clauses in saturation        : 6
% 0.21/0.52  # Processed clauses                    : 28
% 0.21/0.52  # ...of these trivial                  : 0
% 0.21/0.52  # ...subsumed                          : 0
% 0.21/0.52  # ...remaining for further processing  : 28
% 0.21/0.52  # Other redundant clauses eliminated   : 0
% 0.21/0.52  # Clauses deleted for lack of memory   : 0
% 0.21/0.52  # Backward-subsumed                    : 0
% 0.21/0.52  # Backward-rewritten                   : 1
% 0.21/0.52  # Generated clauses                    : 35
% 0.21/0.52  # ...of the previous two non-redundant : 35
% 0.21/0.52  # ...aggressively subsumed             : 0
% 0.21/0.52  # Contextual simplify-reflections      : 0
% 0.21/0.52  # Paramodulations                      : 35
% 0.21/0.52  # Factorizations                       : 0
% 0.21/0.52  # NegExts                              : 0
% 0.21/0.52  # Equation resolutions                 : 0
% 0.21/0.52  # Disequality decompositions           : 0
% 0.21/0.52  # Total rewrite steps                  : 1
% 0.21/0.52  # ...of those cached                   : 0
% 0.21/0.52  # Propositional unsat checks           : 0
% 0.21/0.52  #    Propositional check models        : 0
% 0.21/0.52  #    Propositional check unsatisfiable : 0
% 0.21/0.52  #    Propositional clauses             : 0
% 0.21/0.52  #    Propositional clauses after purity: 0
% 0.21/0.52  #    Propositional unsat core size     : 0
% 0.21/0.52  #    Propositional preprocessing time  : 0.000
% 0.21/0.52  #    Propositional encoding time       : 0.000
% 0.21/0.52  #    Propositional solver time         : 0.000
% 0.21/0.52  #    Success case prop preproc time    : 0.000
% 0.21/0.52  #    Success case prop encoding time   : 0.000
% 0.21/0.52  #    Success case prop solver time     : 0.000
% 0.21/0.52  # Current number of processed clauses  : 21
% 0.21/0.52  #    Positive orientable unit clauses  : 3
% 0.21/0.52  #    Positive unorientable unit clauses: 0
% 0.21/0.52  #    Negative unit clauses             : 0
% 0.21/0.52  #    Non-unit-clauses                  : 18
% 0.21/0.52  # Current number of unprocessed clauses: 19
% 0.21/0.52  # ...number of literals in the above   : 38
% 0.21/0.52  # Current number of archived formulas  : 0
% 0.21/0.52  # Current number of archived clauses   : 7
% 0.21/0.52  # Clause-clause subsumption calls (NU) : 53
% 0.21/0.52  # Rec. Clause-clause subsumption calls : 46
% 0.21/0.52  # Non-unit clause-clause subsumptions  : 0
% 0.21/0.52  # Unit Clause-clause subsumption calls : 21
% 0.21/0.52  # Rewrite failures with RHS unbound    : 0
% 0.21/0.52  # BW rewrite match attempts            : 4
% 0.21/0.52  # BW rewrite match successes           : 1
% 0.21/0.52  # Condensation attempts                : 28
% 0.21/0.52  # Condensation successes               : 0
% 0.21/0.52  # Termbank termtop insertions          : 1440
% 0.21/0.52  # Search garbage collected termcells   : 253
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.004 s
% 0.21/0.52  # System time              : 0.001 s
% 0.21/0.52  # Total time               : 0.006 s
% 0.21/0.52  # Maximum resident set size: 1792 pages
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.010 s
% 0.21/0.52  # System time              : 0.006 s
% 0.21/0.52  # Total time               : 0.017 s
% 0.21/0.52  # Maximum resident set size: 1700 pages
% 0.21/0.52  % E---3.1 exiting
% 0.21/0.52  % E exiting
%------------------------------------------------------------------------------