TSTP Solution File: SEU627^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU627^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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 03:28:40 EDT 2024

% Result   : Theorem 0.22s 0.50s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   36 (   5 unt;  15 typ;   0 def)
%            Number of atoms       :   79 (  11 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  366 (  19   ~;  23   |;   7   &; 289   @)
%                                         (   4 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  10 con; 0-2 aty)
%            Number of variables   :   69 (   0   ^  69   !;   0   ?;  69   :)

% 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,
    powerset: $i > $i ).

thf(decl_26,type,
    subset: $i > $i > $o ).

thf(decl_27,type,
    subsetI2: $o ).

thf(decl_28,type,
    binunion: $i > $i > $i ).

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

thf(decl_30,type,
    upairset2E: $o ).

thf(decl_31,type,
    upairinpowunion: $o ).

thf(decl_32,type,
    esk1_2: $i > $i > $i ).

thf(decl_33,type,
    esk2_0: $i ).

thf(decl_34,type,
    esk3_0: $i ).

thf(decl_35,type,
    esk4_0: $i ).

thf(decl_36,type,
    esk5_0: $i ).

thf(ubforcartprodlem1,conjecture,
    ( subsetI2
   => ( singletoninpowunion
     => ( upairset2E
       => ( upairinpowunion
         => ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) )
       => ( subset @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

thf(singletoninpowunion,axiom,
    ( singletoninpowunion
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(upairset2E,axiom,
    ( upairset2E
  <=> ! [X3: $i,X4: $i,X5: $i] :
        ( ( in @ X5 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) )
       => ( ( X5 = X3 )
          | ( X5 = X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).

thf(upairinpowunion,axiom,
    ( upairinpowunion
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X2 )
           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).

thf(c_0_5,negated_conjecture,
    ~ ( ! [X23: $i,X24: $i] :
          ( ! [X25: $i] :
              ( ( in @ X25 @ X23 )
             => ( in @ X25 @ X24 ) )
         => ( subset @ X23 @ X24 ) )
     => ( ! [X26: $i,X27: $i,X28: $i] :
            ( ( in @ X28 @ X26 )
           => ( in @ ( setadjoin @ X28 @ emptyset ) @ ( powerset @ ( binunion @ X26 @ X27 ) ) ) )
       => ( ! [X29: $i,X30: $i,X31: $i] :
              ( ( in @ X31 @ ( setadjoin @ X29 @ ( setadjoin @ X30 @ emptyset ) ) )
             => ( ( X31 = X29 )
                | ( X31 = X30 ) ) )
         => ( ! [X32: $i,X33: $i,X34: $i] :
                ( ( in @ X34 @ X32 )
               => ! [X35: $i] :
                    ( ( in @ X35 @ X33 )
                   => ( in @ ( setadjoin @ X34 @ ( setadjoin @ X35 @ emptyset ) ) @ ( powerset @ ( binunion @ X32 @ X33 ) ) ) ) )
           => ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ubforcartprodlem1]),subsetI2]),singletoninpowunion]),upairset2E]),upairinpowunion]) ).

thf(c_0_6,negated_conjecture,
    ! [X36: $i,X37: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i] :
      ( ( ( in @ ( esk1_2 @ X36 @ X37 ) @ X36 )
        | ( subset @ X36 @ X37 ) )
      & ( ~ ( in @ ( esk1_2 @ X36 @ X37 ) @ X37 )
        | ( subset @ X36 @ X37 ) )
      & ( ~ ( in @ X41 @ X39 )
        | ( in @ ( setadjoin @ X41 @ emptyset ) @ ( powerset @ ( binunion @ X39 @ X40 ) ) ) )
      & ( ~ ( in @ X44 @ ( setadjoin @ X42 @ ( setadjoin @ X43 @ emptyset ) ) )
        | ( X44 = X42 )
        | ( X44 = X43 ) )
      & ( ~ ( in @ X47 @ X45 )
        | ~ ( in @ X48 @ X46 )
        | ( in @ ( setadjoin @ X47 @ ( setadjoin @ X48 @ emptyset ) ) @ ( powerset @ ( binunion @ X45 @ X46 ) ) ) )
      & ( in @ esk4_0 @ esk2_0 )
      & ( in @ esk5_0 @ esk3_0 )
      & ~ ( subset @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ 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_5])])])])])]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X2 )
      | ( X1 = X3 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
      | ( subset @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
      | ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
        = X1 )
      | ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
        = X2 )
      | ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
        = X1 )
      | ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
      | ~ ( in @ X2 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ~ ( subset @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
      | ~ ( in @ X1 @ X3 )
      | ~ ( in @ X2 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ( ~ ( in @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) )
    | ~ ( in @ ( setadjoin @ esk4_0 @ emptyset ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X4 ) ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_16,negated_conjecture,
    in @ esk5_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_17,negated_conjecture,
    in @ esk4_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_18,negated_conjecture,
    ~ ( in @ ( setadjoin @ esk4_0 @ emptyset ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X3 ) ) )
      | ~ ( in @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : SEU627^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 16:39:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.22/0.49  Running higher-order theorem proving
% 0.22/0.49  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
% 0.22/0.50  # Version: 3.1.0-ho
% 0.22/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.22/0.50  # Starting post_as_ho2 with 300s (1) cores
% 0.22/0.50  # post_as_ho8 with pid 30863 completed with status 0
% 0.22/0.50  # Result found by post_as_ho8
% 0.22/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.50  # Search class: HGUSF-FFSF21-MFFFMFNN
% 0.22/0.50  # partial match(1): HGUSF-FFSF21-SFFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # new_ho_10 with pid 30866 completed with status 0
% 0.22/0.50  # Result found by new_ho_10
% 0.22/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.50  # Search class: HGUSF-FFSF21-MFFFMFNN
% 0.22/0.50  # partial match(1): HGUSF-FFSF21-SFFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # Preprocessing time       : 0.001 s
% 0.22/0.50  # Presaturation interreduction done
% 0.22/0.50  
% 0.22/0.50  # Proof found!
% 0.22/0.50  # SZS status Theorem
% 0.22/0.50  # SZS output start CNFRefutation
% See solution above
% 0.22/0.50  # Parsed axioms                        : 15
% 0.22/0.50  # Removed by relevancy pruning/SinE    : 10
% 0.22/0.50  # Initial clauses                      : 8
% 0.22/0.50  # Removed in clause preprocessing      : 0
% 0.22/0.50  # Initial clauses in saturation        : 8
% 0.22/0.50  # Processed clauses                    : 24
% 0.22/0.50  # ...of these trivial                  : 0
% 0.22/0.50  # ...subsumed                          : 0
% 0.22/0.50  # ...remaining for further processing  : 24
% 0.22/0.50  # Other redundant clauses eliminated   : 2
% 0.22/0.50  # Clauses deleted for lack of memory   : 0
% 0.22/0.50  # Backward-subsumed                    : 1
% 0.22/0.50  # Backward-rewritten                   : 0
% 0.22/0.50  # Generated clauses                    : 21
% 0.22/0.50  # ...of the previous two non-redundant : 18
% 0.22/0.50  # ...aggressively subsumed             : 0
% 0.22/0.50  # Contextual simplify-reflections      : 0
% 0.22/0.50  # Paramodulations                      : 17
% 0.22/0.50  # Factorizations                       : 2
% 0.22/0.50  # NegExts                              : 0
% 0.22/0.50  # Equation resolutions                 : 2
% 0.22/0.50  # Disequality decompositions           : 0
% 0.22/0.50  # Total rewrite steps                  : 3
% 0.22/0.50  # ...of those cached                   : 1
% 0.22/0.50  # Propositional unsat checks           : 0
% 0.22/0.50  #    Propositional check models        : 0
% 0.22/0.50  #    Propositional check unsatisfiable : 0
% 0.22/0.50  #    Propositional clauses             : 0
% 0.22/0.50  #    Propositional clauses after purity: 0
% 0.22/0.50  #    Propositional unsat core size     : 0
% 0.22/0.50  #    Propositional preprocessing time  : 0.000
% 0.22/0.50  #    Propositional encoding time       : 0.000
% 0.22/0.50  #    Propositional solver time         : 0.000
% 0.22/0.50  #    Success case prop preproc time    : 0.000
% 0.22/0.50  #    Success case prop encoding time   : 0.000
% 0.22/0.50  #    Success case prop solver time     : 0.000
% 0.22/0.50  # Current number of processed clauses  : 15
% 0.22/0.50  #    Positive orientable unit clauses  : 3
% 0.22/0.50  #    Positive unorientable unit clauses: 0
% 0.22/0.50  #    Negative unit clauses             : 2
% 0.22/0.50  #    Non-unit-clauses                  : 10
% 0.22/0.50  # Current number of unprocessed clauses: 10
% 0.22/0.50  # ...number of literals in the above   : 30
% 0.22/0.50  # Current number of archived formulas  : 0
% 0.22/0.50  # Current number of archived clauses   : 9
% 0.22/0.50  # Clause-clause subsumption calls (NU) : 34
% 0.22/0.50  # Rec. Clause-clause subsumption calls : 30
% 0.22/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.22/0.50  # Unit Clause-clause subsumption calls : 3
% 0.22/0.50  # Rewrite failures with RHS unbound    : 0
% 0.22/0.50  # BW rewrite match attempts            : 2
% 0.22/0.50  # BW rewrite match successes           : 0
% 0.22/0.50  # Condensation attempts                : 24
% 0.22/0.50  # Condensation successes               : 0
% 0.22/0.50  # Termbank termtop insertions          : 1665
% 0.22/0.50  # Search garbage collected termcells   : 412
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.004 s
% 0.22/0.50  # System time              : 0.003 s
% 0.22/0.50  # Total time               : 0.007 s
% 0.22/0.50  # Maximum resident set size: 1912 pages
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.005 s
% 0.22/0.50  # System time              : 0.005 s
% 0.22/0.50  # Total time               : 0.010 s
% 0.22/0.50  # Maximum resident set size: 1704 pages
% 0.22/0.50  % E---3.1 exiting
% 0.22/0.50  % E exiting
%------------------------------------------------------------------------------