TSTP Solution File: NUM817^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM817^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 08:58:05 EDT 2024

% Result   : Theorem 0.15s 0.42s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   22 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :   34 (  26 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  128 (  19   ~;  11   |;  10   &;  74   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   7   ^  30   !;   2   ?;  39   :)

% 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_2: $i > ( $i > $o ) > $i ).

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

thf(cODD1_def,axiom,
    ( cODD1
    = ( ^ [X1: $i] :
          ~ ( cEVEN1 @ X1 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.zX68GKcGxv/E---3.1_12130.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/sandbox/tmp/tmp.zX68GKcGxv/E---3.1_12130.p',cEVEN1_def) ).

thf(cTHM405,conjecture,
    ( ( ! [X4: $i] :
          ( ( cS @ X4 )
         != c0 )
      & ! [X5: $i,X6: $i] :
          ( ( ( cS @ X5 )
            = ( cS @ X6 ) )
         => ( X5 = X6 ) ) )
   => ? [X1: $i] : ( cODD1 @ X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.zX68GKcGxv/E---3.1_12130.p',cTHM405) ).

thf(c_0_3,plain,
    ( cODD1
    = ( ^ [Z0: $i] :
          ~ ! [X11: $i > $o] :
              ( ( ( X11 @ c0 )
                & ! [X12: $i] :
                    ( ( X11 @ X12 )
                   => ( X11 @ ( cS @ ( cS @ X12 ) ) ) ) )
             => ( X11 @ 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] :
          ~ ! [X11: $i > $o] :
              ( ( ( X11 @ c0 )
                & ! [X12: $i] :
                    ( ( X11 @ X12 )
                   => ( X11 @ ( cS @ ( cS @ X12 ) ) ) ) )
             => ( X11 @ 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 ) ) )
     => ? [X1: $i] :
          ~ ! [X13: $i > $o] :
              ( ( ( X13 @ c0 )
                & ! [X14: $i] :
                    ( ( X13 @ X14 )
                   => ( X13 @ ( cS @ ( cS @ X14 ) ) ) ) )
             => ( X13 @ X1 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM405]),c_0_5])]) ).

thf(c_0_7,negated_conjecture,
    ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i > $o] :
      ( ( ( cS @ X15 )
       != c0 )
      & ( ( ( cS @ X16 )
         != ( cS @ X17 ) )
        | ( X16 = X17 ) )
      & ( ( X19 @ ( esk1_2 @ X18 @ X19 ) )
        | ~ ( X19 @ c0 )
        | ( X19 @ X18 ) )
      & ( ~ ( X19 @ ( cS @ ( cS @ ( esk1_2 @ X18 @ X19 ) ) ) )
        | ~ ( X19 @ c0 )
        | ( X19 @ X18 ) ) ),
    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,
    ! [X1: $i,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X2 @ ( cS @ ( cS @ ( esk1_2 @ X1 @ X2 ) ) ) )
      | ~ ( X2 @ c0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i] :
      ( ( esk2_1 @ ( cS @ X1 ) )
      = X1 ),
    inference(recognize_injectivity,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i] :
      ( ( ( cS
          @ ( cS
            @ ( esk1_2 @ X1
              @ ^ [Z0: $i] : ( Z0 != X1 ) ) ) )
        = X1 )
      | ( c0 = X1 ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: $i] :
      ( ( cS @ X1 )
     != c0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i] :
      ( ( ( cS
          @ ( esk1_2 @ X1
            @ ^ [Z0: $i] : ( Z0 != X1 ) ) )
        = ( esk2_1 @ X1 ) )
      | ( c0 = X1 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i] :
      ( ( c0 = X1 )
      | ( ( esk2_1 @ X1 )
       != c0 ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_15,negated_conjecture,
    $false,
    inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : NUM817^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.05/0.11  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n028.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri May  3 09:39:48 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.41  Running higher-order theorem proving
% 0.15/0.41  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.zX68GKcGxv/E---3.1_12130.p
% 0.15/0.42  # Version: 3.1.0-ho
% 0.15/0.42  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.15/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.42  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.42  # Starting sh4l with 300s (1) cores
% 0.15/0.42  # Starting ho_unfolding_2 with 300s (1) cores
% 0.15/0.42  # post_as_ho5 with pid 12210 completed with status 0
% 0.15/0.42  # Result found by post_as_ho5
% 0.15/0.42  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.15/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.42  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.42  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.15/0.42  # Search class: HGUSF-FFSF21-MSFFMMBN
% 0.15/0.42  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.42  # Starting ho_unfolding_3 with 163s (1) cores
% 0.15/0.42  # ho_unfolding_3 with pid 12213 completed with status 0
% 0.15/0.42  # Result found by ho_unfolding_3
% 0.15/0.42  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.15/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.42  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.42  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.15/0.42  # Search class: HGUSF-FFSF21-MSFFMMBN
% 0.15/0.42  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.42  # Starting ho_unfolding_3 with 163s (1) cores
% 0.15/0.42  # Preprocessing time       : 0.001 s
% 0.15/0.42  # Presaturation interreduction done
% 0.15/0.42  
% 0.15/0.42  # Proof found!
% 0.15/0.42  # SZS status Theorem
% 0.15/0.42  # SZS output start CNFRefutation
% See solution above
% 0.15/0.42  # Parsed axioms                        : 7
% 0.15/0.42  # Removed by relevancy pruning/SinE    : 4
% 0.15/0.42  # Initial clauses                      : 4
% 0.15/0.42  # Removed in clause preprocessing      : 0
% 0.15/0.42  # Initial clauses in saturation        : 4
% 0.15/0.42  # Processed clauses                    : 18
% 0.15/0.42  # ...of these trivial                  : 0
% 0.15/0.42  # ...subsumed                          : 2
% 0.15/0.42  # ...remaining for further processing  : 16
% 0.15/0.42  # Other redundant clauses eliminated   : 4
% 0.15/0.42  # Clauses deleted for lack of memory   : 0
% 0.15/0.42  # Backward-subsumed                    : 0
% 0.15/0.42  # Backward-rewritten                   : 0
% 0.15/0.42  # Generated clauses                    : 29
% 0.15/0.42  # ...of the previous two non-redundant : 19
% 0.15/0.42  # ...aggressively subsumed             : 0
% 0.15/0.42  # Contextual simplify-reflections      : 0
% 0.15/0.42  # Paramodulations                      : 13
% 0.15/0.42  # Factorizations                       : 0
% 0.15/0.42  # NegExts                              : 1
% 0.15/0.42  # Equation resolutions                 : 5
% 0.15/0.42  # Disequality decompositions           : 0
% 0.15/0.42  # Total rewrite steps                  : 0
% 0.15/0.42  # ...of those cached                   : 0
% 0.15/0.42  # Propositional unsat checks           : 0
% 0.15/0.42  #    Propositional check models        : 0
% 0.15/0.42  #    Propositional check unsatisfiable : 0
% 0.15/0.42  #    Propositional clauses             : 0
% 0.15/0.42  #    Propositional clauses after purity: 0
% 0.15/0.42  #    Propositional unsat core size     : 0
% 0.15/0.42  #    Propositional preprocessing time  : 0.000
% 0.15/0.42  #    Propositional encoding time       : 0.000
% 0.15/0.42  #    Propositional solver time         : 0.000
% 0.15/0.42  #    Success case prop preproc time    : 0.000
% 0.15/0.42  #    Success case prop encoding time   : 0.000
% 0.15/0.42  #    Success case prop solver time     : 0.000
% 0.15/0.42  # Current number of processed clauses  : 11
% 0.15/0.42  #    Positive orientable unit clauses  : 1
% 0.15/0.42  #    Positive unorientable unit clauses: 0
% 0.15/0.42  #    Negative unit clauses             : 1
% 0.15/0.42  #    Non-unit-clauses                  : 9
% 0.15/0.42  # Current number of unprocessed clauses: 9
% 0.15/0.42  # ...number of literals in the above   : 22
% 0.15/0.42  # Current number of archived formulas  : 0
% 0.15/0.42  # Current number of archived clauses   : 5
% 0.15/0.42  # Clause-clause subsumption calls (NU) : 12
% 0.15/0.42  # Rec. Clause-clause subsumption calls : 12
% 0.15/0.42  # Non-unit clause-clause subsumptions  : 0
% 0.15/0.42  # Unit Clause-clause subsumption calls : 0
% 0.15/0.42  # Rewrite failures with RHS unbound    : 0
% 0.15/0.42  # BW rewrite match attempts            : 0
% 0.15/0.42  # BW rewrite match successes           : 0
% 0.15/0.42  # Condensation attempts                : 18
% 0.15/0.42  # Condensation successes               : 0
% 0.15/0.42  # Termbank termtop insertions          : 1004
% 0.15/0.42  # Search garbage collected termcells   : 214
% 0.15/0.42  
% 0.15/0.42  # -------------------------------------------------
% 0.15/0.42  # User time                : 0.004 s
% 0.15/0.42  # System time              : 0.001 s
% 0.15/0.42  # Total time               : 0.005 s
% 0.15/0.42  # Maximum resident set size: 1716 pages
% 0.15/0.42  
% 0.15/0.42  # -------------------------------------------------
% 0.15/0.42  # User time                : 0.006 s
% 0.15/0.42  # System time              : 0.001 s
% 0.15/0.42  # Total time               : 0.007 s
% 0.15/0.42  # Maximum resident set size: 1708 pages
% 0.15/0.42  % E---3.1 exiting
% 0.15/0.42  % E exiting
%------------------------------------------------------------------------------