TSTP Solution File: PUZ110^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : PUZ110^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 02:25:12 EDT 2024

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   23 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :   26 (   2 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  214 (  17   ~;  14   |;  13   &; 160   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   29 (   4   ^  25   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    c1: $i ).

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

thf(decl_24,type,
    cCKB6_BLACK: $i > $i > $o ).

thf(decl_25,type,
    esk1_0: $i ).

thf(decl_26,type,
    esk2_0: $i ).

thf(decl_27,type,
    esk3_1: ( $i > $i > $o ) > $i ).

thf(decl_28,type,
    esk4_1: ( $i > $i > $o ) > $i ).

thf(decl_29,type,
    epred1_0: $i > $i > $o ).

thf(cCKB6_BLACK_def,axiom,
    ( cCKB6_BLACK
    = ( ^ [X1: $i,X2: $i] :
        ! [X3: $i > $i > $o] :
          ( ( ( X3 @ c1 @ c1 )
            & ! [X4: $i,X5: $i] :
                ( ( X3 @ X4 @ X5 )
               => ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
                  & ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
         => ( X3 @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_BLACK_def) ).

thf(cCKB6_L8000,conjecture,
    ! [X4: $i,X5: $i] :
      ( ( cCKB6_BLACK @ X4 @ X5 )
     => ( cCKB6_BLACK @ ( s @ ( s @ X4 ) ) @ X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L8000) ).

thf(c_0_2,plain,
    ( cCKB6_BLACK
    = ( ^ [Z0: $i,Z1: $i] :
        ! [X3: $i > $i > $o] :
          ( ( ( X3 @ c1 @ c1 )
            & ! [X4: $i,X5: $i] :
                ( ( X3 @ X4 @ X5 )
               => ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
                  & ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
         => ( X3 @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cCKB6_BLACK_def]) ).

thf(c_0_3,negated_conjecture,
    ~ ! [X4: $i,X5: $i] :
        ( ! [X8: $i > $i > $o] :
            ( ( ( X8 @ c1 @ c1 )
              & ! [X9: $i,X10: $i] :
                  ( ( X8 @ X9 @ X10 )
                 => ( ( X8 @ ( s @ ( s @ X9 ) ) @ X10 )
                    & ( X8 @ ( s @ X9 ) @ ( s @ X10 ) ) ) ) )
           => ( X8 @ X4 @ X5 ) )
       => ! [X11: $i > $i > $o] :
            ( ( ( X11 @ c1 @ c1 )
              & ! [X12: $i,X13: $i] :
                  ( ( X11 @ X12 @ X13 )
                 => ( ( X11 @ ( s @ ( s @ X12 ) ) @ X13 )
                    & ( X11 @ ( s @ X12 ) @ ( s @ X13 ) ) ) ) )
           => ( X11 @ ( s @ ( s @ X4 ) ) @ X5 ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cCKB6_L8000]),c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X16: $i > $i > $o,X20: $i,X21: $i] :
      ( ( ( X16 @ ( esk3_1 @ X16 ) @ ( esk4_1 @ X16 ) )
        | ~ ( X16 @ c1 @ c1 )
        | ( X16 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( X16 @ ( s @ ( s @ ( esk3_1 @ X16 ) ) ) @ ( esk4_1 @ X16 ) )
        | ~ ( X16 @ ( s @ ( esk3_1 @ X16 ) ) @ ( s @ ( esk4_1 @ X16 ) ) )
        | ~ ( X16 @ c1 @ c1 )
        | ( X16 @ esk1_0 @ esk2_0 ) )
      & ( epred1_0 @ c1 @ c1 )
      & ( ( epred1_0 @ ( s @ ( s @ X20 ) ) @ X21 )
        | ~ ( epred1_0 @ X20 @ X21 ) )
      & ( ( epred1_0 @ ( s @ X20 ) @ ( s @ X21 ) )
        | ~ ( epred1_0 @ X20 @ X21 ) )
      & ~ ( epred1_0 @ ( s @ ( s @ esk1_0 ) ) @ esk2_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_3])])])])])]) ).

thf(c_0_5,negated_conjecture,
    ~ ( epred1_0 @ ( s @ ( s @ esk1_0 ) ) @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( epred1_0 @ ( s @ ( s @ X1 ) ) @ X2 )
      | ~ ( epred1_0 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_7,negated_conjecture,
    ! [X3: $i > $i > $o] :
      ( ( X3 @ ( esk3_1 @ X3 ) @ ( esk4_1 @ X3 ) )
      | ( X3 @ esk1_0 @ esk2_0 )
      | ~ ( X3 @ c1 @ c1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_8,negated_conjecture,
    epred1_0 @ c1 @ c1,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_9,negated_conjecture,
    ~ ( epred1_0 @ esk1_0 @ esk2_0 ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ! [X3: $i > $i > $o] :
      ( ( X3 @ esk1_0 @ esk2_0 )
      | ~ ( X3 @ ( s @ ( s @ ( esk3_1 @ X3 ) ) ) @ ( esk4_1 @ X3 ) )
      | ~ ( X3 @ ( s @ ( esk3_1 @ X3 ) ) @ ( s @ ( esk4_1 @ X3 ) ) )
      | ~ ( X3 @ c1 @ c1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( epred1_0 @ ( s @ X1 ) @ ( s @ X2 ) )
      | ~ ( epred1_0 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_12,negated_conjecture,
    epred1_0 @ ( esk3_1 @ epred1_0 ) @ ( esk4_1 @ epred1_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

thf(c_0_13,negated_conjecture,
    ~ ( epred1_0 @ ( s @ ( s @ ( esk3_1 @ epred1_0 ) ) ) @ ( esk4_1 @ epred1_0 ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]),c_0_12])]),c_0_9]) ).

thf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_6]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PUZ110^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 10:26:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.19/0.46  Running higher-order theorem proving
% 0.19/0.46  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
% 0.19/0.48  # Version: 3.1.0-ho
% 0.19/0.48  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting post_as_ho5 with 300s (1) cores
% 0.19/0.48  # Starting sh4l with 300s (1) cores
% 0.19/0.48  # Starting ho_unfolding_2 with 300s (1) cores
% 0.19/0.48  # post_as_ho5 with pid 16670 completed with status 0
% 0.19/0.48  # Result found by post_as_ho5
% 0.19/0.48  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting post_as_ho5 with 300s (1) cores
% 0.19/0.48  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.19/0.48  # Search class: HGUNF-FFSF11-MSFFMSBN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting new_ho_10_unif with 181s (1) cores
% 0.19/0.48  # new_ho_10_unif with pid 16673 completed with status 0
% 0.19/0.48  # Result found by new_ho_10_unif
% 0.19/0.48  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting post_as_ho5 with 300s (1) cores
% 0.19/0.48  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.19/0.48  # Search class: HGUNF-FFSF11-MSFFMSBN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting new_ho_10_unif with 181s (1) cores
% 0.19/0.48  # Preprocessing time       : 0.001 s
% 0.19/0.48  # Presaturation interreduction done
% 0.19/0.48  
% 0.19/0.48  # Proof found!
% 0.19/0.48  # SZS status Theorem
% 0.19/0.48  # SZS output start CNFRefutation
% See solution above
% 0.19/0.48  # Parsed axioms                        : 5
% 0.19/0.48  # Removed by relevancy pruning/SinE    : 3
% 0.19/0.48  # Initial clauses                      : 6
% 0.19/0.48  # Removed in clause preprocessing      : 0
% 0.19/0.48  # Initial clauses in saturation        : 6
% 0.19/0.48  # Processed clauses                    : 16
% 0.19/0.48  # ...of these trivial                  : 0
% 0.19/0.48  # ...subsumed                          : 0
% 0.19/0.48  # ...remaining for further processing  : 16
% 0.19/0.48  # Other redundant clauses eliminated   : 0
% 0.19/0.48  # Clauses deleted for lack of memory   : 0
% 0.19/0.48  # Backward-subsumed                    : 0
% 0.19/0.48  # Backward-rewritten                   : 0
% 0.19/0.48  # Generated clauses                    : 23
% 0.19/0.48  # ...of the previous two non-redundant : 18
% 0.19/0.48  # ...aggressively subsumed             : 0
% 0.19/0.48  # Contextual simplify-reflections      : 0
% 0.19/0.48  # Paramodulations                      : 21
% 0.19/0.48  # Factorizations                       : 0
% 0.19/0.48  # NegExts                              : 0
% 0.19/0.48  # Equation resolutions                 : 2
% 0.19/0.48  # Disequality decompositions           : 0
% 0.19/0.48  # Total rewrite steps                  : 9
% 0.19/0.48  # ...of those cached                   : 7
% 0.19/0.48  # Propositional unsat checks           : 0
% 0.19/0.48  #    Propositional check models        : 0
% 0.19/0.48  #    Propositional check unsatisfiable : 0
% 0.19/0.48  #    Propositional clauses             : 0
% 0.19/0.48  #    Propositional clauses after purity: 0
% 0.19/0.48  #    Propositional unsat core size     : 0
% 0.19/0.48  #    Propositional preprocessing time  : 0.000
% 0.19/0.48  #    Propositional encoding time       : 0.000
% 0.19/0.48  #    Propositional solver time         : 0.000
% 0.19/0.48  #    Success case prop preproc time    : 0.000
% 0.19/0.48  #    Success case prop encoding time   : 0.000
% 0.19/0.48  #    Success case prop solver time     : 0.000
% 0.19/0.48  # Current number of processed clauses  : 10
% 0.19/0.48  #    Positive orientable unit clauses  : 2
% 0.19/0.48  #    Positive unorientable unit clauses: 0
% 0.19/0.48  #    Negative unit clauses             : 3
% 0.19/0.48  #    Non-unit-clauses                  : 5
% 0.19/0.48  # Current number of unprocessed clauses: 14
% 0.19/0.48  # ...number of literals in the above   : 42
% 0.19/0.48  # Current number of archived formulas  : 0
% 0.19/0.48  # Current number of archived clauses   : 6
% 0.19/0.48  # Clause-clause subsumption calls (NU) : 8
% 0.19/0.48  # Rec. Clause-clause subsumption calls : 8
% 0.19/0.48  # Non-unit clause-clause subsumptions  : 0
% 0.19/0.48  # Unit Clause-clause subsumption calls : 1
% 0.19/0.48  # Rewrite failures with RHS unbound    : 0
% 0.19/0.48  # BW rewrite match attempts            : 0
% 0.19/0.48  # BW rewrite match successes           : 0
% 0.19/0.48  # Condensation attempts                : 16
% 0.19/0.48  # Condensation successes               : 0
% 0.19/0.48  # Termbank termtop insertions          : 3835
% 0.19/0.48  # Search garbage collected termcells   : 280
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.006 s
% 0.19/0.48  # System time              : 0.001 s
% 0.19/0.48  # Total time               : 0.007 s
% 0.19/0.48  # Maximum resident set size: 1768 pages
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.007 s
% 0.19/0.48  # System time              : 0.003 s
% 0.19/0.48  # Total time               : 0.010 s
% 0.19/0.48  # Maximum resident set size: 1720 pages
% 0.19/0.48  % E---3.1 exiting
% 0.19/0.48  % E exiting
%------------------------------------------------------------------------------