TSTP Solution File: NUM816^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 01:17:25 EDT 2024

% Result   : Theorem 0.21s 0.50s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   20 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   28 (  20 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  121 (  17   ~;   8   |;  10   &;  72   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   31 (   6   ^  25   !;   0   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    c0: $i ).

thf(decl_23,type,
    cS: $i > $i ).

thf(decl_24,type,
    cEVEN1: $i > $o ).

thf(decl_25,type,
    cODD1: $i > $o ).

thf(decl_26,type,
    esk1_1: ( $i > $o ) > $i ).

thf(decl_27,type,
    esk2_1: $i > $i ).

thf(cODD1_def,axiom,
    ( cODD1
    = ( ^ [X1: $i] :
          ~ ( cEVEN1 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cODD1_def) ).

thf(cEVEN1_def,axiom,
    ( cEVEN1
    = ( ^ [X1: $i] :
        ! [X2: $i > $o] :
          ( ( ( X2 @ c0 )
            & ! [X3: $i] :
                ( ( X2 @ X3 )
               => ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
         => ( X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEVEN1_def) ).

thf(cTHM406,conjecture,
    ( ( ! [X4: $i] :
          ( ( cS @ X4 )
         != c0 )
      & ! [X5: $i,X6: $i] :
          ( ( ( cS @ X5 )
            = ( cS @ X6 ) )
         => ( X5 = X6 ) ) )
   => ( cODD1 @ ( cS @ c0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM406) ).

thf(c_0_3,plain,
    ( cODD1
    = ( ^ [Z0: $i] :
          ~ ! [X10: $i > $o] :
              ( ( ( X10 @ c0 )
                & ! [X11: $i] :
                    ( ( X10 @ X11 )
                   => ( X10 @ ( cS @ ( cS @ X11 ) ) ) ) )
             => ( X10 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cODD1_def]) ).

thf(c_0_4,plain,
    ( cEVEN1
    = ( ^ [Z0: $i] :
        ! [X2: $i > $o] :
          ( ( ( X2 @ c0 )
            & ! [X3: $i] :
                ( ( X2 @ X3 )
               => ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
         => ( X2 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cEVEN1_def]) ).

thf(c_0_5,plain,
    ( cODD1
    = ( ^ [Z0: $i] :
          ~ ! [X10: $i > $o] :
              ( ( ( X10 @ c0 )
                & ! [X11: $i] :
                    ( ( X10 @ X11 )
                   => ( X10 @ ( cS @ ( cS @ X11 ) ) ) ) )
             => ( X10 @ Z0 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_6,negated_conjecture,
    ~ ( ( ! [X4: $i] :
            ( ( cS @ X4 )
           != c0 )
        & ! [X5: $i,X6: $i] :
            ( ( ( cS @ X5 )
              = ( cS @ X6 ) )
           => ( X5 = X6 ) ) )
     => ~ ! [X12: $i > $o] :
            ( ( ( X12 @ c0 )
              & ! [X13: $i] :
                  ( ( X12 @ X13 )
                 => ( X12 @ ( cS @ ( cS @ X13 ) ) ) ) )
           => ( X12 @ ( cS @ c0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM406]),c_0_5])]) ).

thf(c_0_7,negated_conjecture,
    ! [X14: $i,X15: $i,X16: $i,X17: $i > $o] :
      ( ( ( cS @ X14 )
       != c0 )
      & ( ( ( cS @ X15 )
         != ( cS @ X16 ) )
        | ( X15 = X16 ) )
      & ( ( X17 @ ( esk1_1 @ X17 ) )
        | ~ ( X17 @ c0 )
        | ( X17 @ ( cS @ c0 ) ) )
      & ( ~ ( X17 @ ( cS @ ( cS @ ( esk1_1 @ X17 ) ) ) )
        | ~ ( X17 @ c0 )
        | ( X17 @ ( cS @ c0 ) ) ) ),
    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_6])])])])])]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( ( cS @ X1 )
       != ( cS @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( X2 @ ( cS @ c0 ) )
      | ~ ( X2 @ ( cS @ ( cS @ ( esk1_1 @ X2 ) ) ) )
      | ~ ( X2 @ c0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i] :
      ( ( cS @ X1 )
     != c0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i] :
      ( ( esk2_1 @ ( cS @ X1 ) )
      = X1 ),
    inference(recognize_injectivity,[status(thm)],[c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ( ( cS
      @ ( cS
        @ ( esk1_1
          @ ^ [Z0: $i] :
              ( Z0
             != ( cS @ c0 ) ) ) ) )
    = ( cS @ c0 ) ),
    inference(sr,[status(thm)],[inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]),c_0_10]) ).

thf(c_0_13,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n023.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   : Mon May 20 04:21:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  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
% 0.21/0.50  # Version: 3.1.0-ho
% 0.21/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.21/0.50  # Starting sh4l with 300s (1) cores
% 0.21/0.50  # Starting ho_unfolding_2 with 300s (1) cores
% 0.21/0.50  # post_as_ho5 with pid 30961 completed with status 0
% 0.21/0.50  # Result found by post_as_ho5
% 0.21/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.21/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.21/0.50  # Search class: HGUSF-FFSF11-MSFFMMBN
% 0.21/0.50  # partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.21/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting ho_unfolding_3 with 163s (1) cores
% 0.21/0.50  # ho_unfolding_3 with pid 30964 completed with status 0
% 0.21/0.50  # Result found by ho_unfolding_3
% 0.21/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.21/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.21/0.50  # Search class: HGUSF-FFSF11-MSFFMMBN
% 0.21/0.50  # partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.21/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting ho_unfolding_3 with 163s (1) cores
% 0.21/0.50  # Preprocessing time       : 0.001 s
% 0.21/0.50  # Presaturation interreduction done
% 0.21/0.50  
% 0.21/0.50  # Proof found!
% 0.21/0.50  # SZS status Theorem
% 0.21/0.50  # SZS output start CNFRefutation
% See solution above
% 0.21/0.50  # Parsed axioms                        : 7
% 0.21/0.50  # Removed by relevancy pruning/SinE    : 4
% 0.21/0.50  # Initial clauses                      : 4
% 0.21/0.50  # Removed in clause preprocessing      : 0
% 0.21/0.50  # Initial clauses in saturation        : 4
% 0.21/0.50  # Processed clauses                    : 14
% 0.21/0.50  # ...of these trivial                  : 0
% 0.21/0.50  # ...subsumed                          : 2
% 0.21/0.50  # ...remaining for further processing  : 12
% 0.21/0.50  # Other redundant clauses eliminated   : 0
% 0.21/0.50  # Clauses deleted for lack of memory   : 0
% 0.21/0.50  # Backward-subsumed                    : 0
% 0.21/0.50  # Backward-rewritten                   : 0
% 0.21/0.50  # Generated clauses                    : 14
% 0.21/0.50  # ...of the previous two non-redundant : 9
% 0.21/0.50  # ...aggressively subsumed             : 0
% 0.21/0.50  # Contextual simplify-reflections      : 0
% 0.21/0.50  # Paramodulations                      : 6
% 0.21/0.50  # Factorizations                       : 0
% 0.21/0.50  # NegExts                              : 0
% 0.21/0.50  # Equation resolutions                 : 1
% 0.21/0.50  # Disequality decompositions           : 0
% 0.21/0.50  # Total rewrite steps                  : 1
% 0.21/0.50  # ...of those cached                   : 0
% 0.21/0.50  # Propositional unsat checks           : 0
% 0.21/0.50  #    Propositional check models        : 0
% 0.21/0.50  #    Propositional check unsatisfiable : 0
% 0.21/0.50  #    Propositional clauses             : 0
% 0.21/0.50  #    Propositional clauses after purity: 0
% 0.21/0.50  #    Propositional unsat core size     : 0
% 0.21/0.50  #    Propositional preprocessing time  : 0.000
% 0.21/0.50  #    Propositional encoding time       : 0.000
% 0.21/0.50  #    Propositional solver time         : 0.000
% 0.21/0.50  #    Success case prop preproc time    : 0.000
% 0.21/0.50  #    Success case prop encoding time   : 0.000
% 0.21/0.50  #    Success case prop solver time     : 0.000
% 0.21/0.50  # Current number of processed clauses  : 8
% 0.21/0.50  #    Positive orientable unit clauses  : 3
% 0.21/0.50  #    Positive unorientable unit clauses: 0
% 0.21/0.50  #    Negative unit clauses             : 2
% 0.21/0.50  #    Non-unit-clauses                  : 3
% 0.21/0.50  # Current number of unprocessed clauses: 1
% 0.21/0.50  # ...number of literals in the above   : 2
% 0.21/0.50  # Current number of archived formulas  : 0
% 0.21/0.50  # Current number of archived clauses   : 4
% 0.21/0.50  # Clause-clause subsumption calls (NU) : 4
% 0.21/0.50  # Rec. Clause-clause subsumption calls : 4
% 0.21/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.21/0.50  # Unit Clause-clause subsumption calls : 0
% 0.21/0.50  # Rewrite failures with RHS unbound    : 0
% 0.21/0.50  # BW rewrite match attempts            : 1
% 0.21/0.50  # BW rewrite match successes           : 0
% 0.21/0.50  # Condensation attempts                : 14
% 0.21/0.50  # Condensation successes               : 0
% 0.21/0.50  # Termbank termtop insertions          : 772
% 0.21/0.50  # Search garbage collected termcells   : 201
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.005 s
% 0.21/0.50  # System time              : 0.001 s
% 0.21/0.50  # Total time               : 0.006 s
% 0.21/0.50  # Maximum resident set size: 1744 pages
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.005 s
% 0.21/0.50  # System time              : 0.004 s
% 0.21/0.50  # Total time               : 0.009 s
% 0.21/0.50  # Maximum resident set size: 1704 pages
% 0.21/0.50  % E---3.1 exiting
% 0.21/0.50  % E exiting
%------------------------------------------------------------------------------