TSTP Solution File: NUM827^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM827^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 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 01:17:26 EDT 2024

% Result   : Theorem 0.68s 0.63s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   26 (   8 unt;   9 typ;   0 def)
%            Number of atoms       :   46 (  39 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  199 (  11   ~;  10   |;  10   &; 159   @)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   42 (   7   ^  35   !;   0   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    n: $tType ).

thf(decl_22,type,
    c0: n ).

thf(decl_23,type,
    cS: n > n ).

thf(decl_24,type,
    c_plus: n > n > n ).

thf(decl_25,type,
    cPA_1: $o ).

thf(decl_26,type,
    cPA_2: $o ).

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

thf(decl_28,type,
    esk1_2: ( n > n ) > ( n > n ) > n ).

thf(decl_29,type,
    esk2_0: n ).

thf(cPA_THM2,conjecture,
    ( ( cPA_1
      & cPA_2
      & cPA_IND_EQ )
   => ! [X1: n] :
        ( ( c_plus @ X1 @ c0 )
        = ( c_plus @ c0 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_THM2) ).

thf(cPA_IND_EQ_def,axiom,
    ( cPA_IND_EQ
  <=> ! [X3: n > n,X4: n > n] :
        ( ( ( ( X3 @ c0 )
            = ( X4 @ c0 ) )
          & ! [X1: n] :
              ( ( ( X3 @ X1 )
                = ( X4 @ X1 ) )
             => ( ( X3 @ ( cS @ X1 ) )
                = ( X4 @ ( cS @ X1 ) ) ) ) )
       => ! [X1: n] :
            ( ( X3 @ X1 )
            = ( X4 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_IND_EQ_def) ).

thf(cPA_1_def,axiom,
    ( cPA_1
  <=> ! [X1: n] :
        ( ( c_plus @ X1 @ c0 )
        = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_1_def) ).

thf(cPA_2_def,axiom,
    ( cPA_2
  <=> ! [X1: n,X2: n] :
        ( ( c_plus @ X1 @ ( cS @ X2 ) )
        = ( cS @ ( c_plus @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_2_def) ).

thf(c_0_4,negated_conjecture,
    ~ ( ( ! [X13: n] :
            ( ( c_plus @ X13 @ c0 )
            = X13 )
        & ! [X14: n,X15: n] :
            ( ( c_plus @ X14 @ ( cS @ X15 ) )
            = ( cS @ ( c_plus @ X14 @ X15 ) ) )
        & ! [X16: n > n,X17: n > n] :
            ( ( ( ( X16 @ c0 )
                = ( X17 @ c0 ) )
              & ! [X18: n] :
                  ( ( ( X16 @ X18 )
                    = ( X17 @ X18 ) )
                 => ( ( X16 @ ( cS @ X18 ) )
                    = ( X17 @ ( cS @ X18 ) ) ) ) )
           => ! [X19: n] :
                ( ( X16 @ X19 )
                = ( X17 @ X19 ) ) ) )
     => ! [X1: n] :
          ( ( c_plus @ X1 @ c0 )
          = ( c_plus @ c0 @ X1 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cPA_THM2]),cPA_IND_EQ_def]),cPA_1_def]),cPA_2_def]) ).

thf(c_0_5,negated_conjecture,
    ! [X20: n,X21: n,X22: n,X23: n > n,X24: n > n,X26: n] :
      ( ( ( c_plus @ X20 @ c0 )
        = X20 )
      & ( ( c_plus @ X21 @ ( cS @ X22 ) )
        = ( cS @ ( c_plus @ X21 @ X22 ) ) )
      & ( ( ( X23 @ ( esk1_2 @ X23 @ X24 ) )
          = ( X24 @ ( esk1_2 @ X23 @ X24 ) ) )
        | ( ( X23 @ c0 )
         != ( X24 @ c0 ) )
        | ( ( X23 @ X26 )
          = ( X24 @ X26 ) ) )
      & ( ( ( X23 @ ( cS @ ( esk1_2 @ X23 @ X24 ) ) )
         != ( X24 @ ( cS @ ( esk1_2 @ X23 @ X24 ) ) ) )
        | ( ( X23 @ c0 )
         != ( X24 @ c0 ) )
        | ( ( X23 @ X26 )
          = ( X24 @ X26 ) ) )
      & ( ( c_plus @ esk2_0 @ c0 )
       != ( c_plus @ c0 @ 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_4])])])])])]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: n,X3: n > n,X4: n > n] :
      ( ( ( X3 @ ( esk1_2 @ X3 @ X4 ) )
        = ( X4 @ ( esk1_2 @ X3 @ X4 ) ) )
      | ( ( X3 @ X1 )
        = ( X4 @ X1 ) )
      | ( ( X3 @ c0 )
       != ( X4 @ c0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: n] :
      ( ( c_plus @ X1 @ c0 )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: n,X3: n > n,X4: n > n] :
      ( ( ( X3
          @ ( esk1_2 @ X3
            @ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) )
        = ( c_plus
          @ ( X4
            @ ( esk1_2 @ X3
              @ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) )
          @ ( esk1_2 @ X3
            @ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) ) )
      | ( ( X3 @ X1 )
        = ( c_plus @ ( X4 @ X1 ) @ X1 ) )
      | ( ( X3 @ c0 )
       != ( X4 @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: n,X2: n] :
      ( ( c_plus @ X1 @ ( cS @ X2 ) )
      = ( cS @ ( c_plus @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_10,negated_conjecture,
    ( ( c_plus @ c0
      @ ( esk1_2
        @ ^ [Z0: n] : Z0
        @ ( c_plus @ c0 ) ) )
    = ( esk1_2
      @ ^ [Z0: n] : Z0
      @ ( c_plus @ c0 ) ) ),
    inference(condense,[status(thm)],[inference(er,[status(thm)],[c_0_8])]) ).

thf(c_0_11,negated_conjecture,
    ( ( c_plus @ esk2_0 @ c0 )
   != ( c_plus @ c0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: n,X3: n > n,X4: n > n] :
      ( ( ( X3 @ X1 )
        = ( X4 @ X1 ) )
      | ( ( X3 @ ( cS @ ( esk1_2 @ X3 @ X4 ) ) )
       != ( X4 @ ( cS @ ( esk1_2 @ X3 @ X4 ) ) ) )
      | ( ( X3 @ c0 )
       != ( X4 @ c0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_13,negated_conjecture,
    ( ( c_plus @ c0
      @ ( cS
        @ ( esk1_2
          @ ^ [Z0: n] : Z0
          @ ( c_plus @ c0 ) ) ) )
    = ( cS
      @ ( esk1_2
        @ ^ [Z0: n] : Z0
        @ ( c_plus @ c0 ) ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_14,negated_conjecture,
    ( ( c_plus @ c0 @ esk2_0 )
   != esk2_0 ),
    inference(rw,[status(thm)],[c_0_11,c_0_7]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: n] :
      ( ( c_plus @ c0 @ X1 )
      = X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_7])]) ).

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
% 0.07/0.12  % Problem    : NUM827^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 06:26:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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
% 0.68/0.63  # Version: 3.1.0-ho
% 0.68/0.63  # Preprocessing class: HSSSSLSSSLSNSFA.
% 0.68/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.63  # Starting post_as_ho5 with 1500s (5) cores
% 0.68/0.63  # Starting post_as_ho10 with 300s (1) cores
% 0.68/0.63  # Starting post_as_ho4 with 300s (1) cores
% 0.68/0.63  # Starting sh5l with 300s (1) cores
% 0.68/0.63  # post_as_ho5 with pid 18774 completed with status 0
% 0.68/0.63  # Result found by post_as_ho5
% 0.68/0.63  # Preprocessing class: HSSSSLSSSLSNSFA.
% 0.68/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.63  # Starting post_as_ho5 with 1500s (5) cores
% 0.68/0.63  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.68/0.63  # Search class: HGUPS-FFSF21-MSFFMSNN
% 0.68/0.63  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.68/0.63  # Starting post_as_ho10 with 500s (1) cores
% 0.68/0.63  # Starting post_as_ho5 with 251s (1) cores
% 0.68/0.63  # Starting post_as_ho4 with 251s (1) cores
% 0.68/0.63  # Starting new_ho_10_unif with 251s (1) cores
% 0.68/0.63  # Starting lpo8_s with 247s (1) cores
% 0.68/0.63  # new_ho_10_unif with pid 18782 completed with status 0
% 0.68/0.63  # Result found by new_ho_10_unif
% 0.68/0.63  # Preprocessing class: HSSSSLSSSLSNSFA.
% 0.68/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.63  # Starting post_as_ho5 with 1500s (5) cores
% 0.68/0.63  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.68/0.63  # Search class: HGUPS-FFSF21-MSFFMSNN
% 0.68/0.63  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.68/0.63  # Starting post_as_ho10 with 500s (1) cores
% 0.68/0.63  # Starting post_as_ho5 with 251s (1) cores
% 0.68/0.63  # Starting post_as_ho4 with 251s (1) cores
% 0.68/0.63  # Starting new_ho_10_unif with 251s (1) cores
% 0.68/0.63  # Preprocessing time       : 0.001 s
% 0.68/0.63  # Presaturation interreduction done
% 0.68/0.63  
% 0.68/0.63  # Proof found!
% 0.68/0.63  # SZS status Theorem
% 0.68/0.63  # SZS output start CNFRefutation
% See solution above
% 0.68/0.63  # Parsed axioms                        : 11
% 0.68/0.63  # Removed by relevancy pruning/SinE    : 7
% 0.68/0.63  # Initial clauses                      : 5
% 0.68/0.63  # Removed in clause preprocessing      : 0
% 0.68/0.63  # Initial clauses in saturation        : 5
% 0.68/0.63  # Processed clauses                    : 118
% 0.68/0.63  # ...of these trivial                  : 8
% 0.68/0.63  # ...subsumed                          : 17
% 0.68/0.63  # ...remaining for further processing  : 93
% 0.68/0.63  # Other redundant clauses eliminated   : 64
% 0.68/0.63  # Clauses deleted for lack of memory   : 0
% 0.68/0.63  # Backward-subsumed                    : 3
% 0.68/0.63  # Backward-rewritten                   : 18
% 0.68/0.63  # Generated clauses                    : 1472
% 0.68/0.63  # ...of the previous two non-redundant : 1125
% 0.68/0.63  # ...aggressively subsumed             : 0
% 0.68/0.63  # Contextual simplify-reflections      : 0
% 0.68/0.63  # Paramodulations                      : 1179
% 0.68/0.63  # Factorizations                       : 9
% 0.68/0.63  # NegExts                              : 0
% 0.68/0.63  # Equation resolutions                 : 284
% 0.68/0.63  # Disequality decompositions           : 0
% 0.68/0.63  # Total rewrite steps                  : 785
% 0.68/0.63  # ...of those cached                   : 599
% 0.68/0.63  # Propositional unsat checks           : 0
% 0.68/0.63  #    Propositional check models        : 0
% 0.68/0.63  #    Propositional check unsatisfiable : 0
% 0.68/0.63  #    Propositional clauses             : 0
% 0.68/0.63  #    Propositional clauses after purity: 0
% 0.68/0.63  #    Propositional unsat core size     : 0
% 0.68/0.63  #    Propositional preprocessing time  : 0.000
% 0.68/0.63  #    Propositional encoding time       : 0.000
% 0.68/0.63  #    Propositional solver time         : 0.000
% 0.68/0.63  #    Success case prop preproc time    : 0.000
% 0.68/0.63  #    Success case prop encoding time   : 0.000
% 0.68/0.63  #    Success case prop solver time     : 0.000
% 0.68/0.63  # Current number of processed clauses  : 67
% 0.68/0.63  #    Positive orientable unit clauses  : 20
% 0.68/0.63  #    Positive unorientable unit clauses: 0
% 0.68/0.63  #    Negative unit clauses             : 0
% 0.68/0.63  #    Non-unit-clauses                  : 47
% 0.68/0.63  # Current number of unprocessed clauses: 943
% 0.68/0.63  # ...number of literals in the above   : 2756
% 0.68/0.63  # Current number of archived formulas  : 0
% 0.68/0.63  # Current number of archived clauses   : 26
% 0.68/0.63  # Clause-clause subsumption calls (NU) : 368
% 0.68/0.63  # Rec. Clause-clause subsumption calls : 368
% 0.68/0.63  # Non-unit clause-clause subsumptions  : 19
% 0.68/0.63  # Unit Clause-clause subsumption calls : 30
% 0.68/0.63  # Rewrite failures with RHS unbound    : 0
% 0.68/0.63  # BW rewrite match attempts            : 70
% 0.68/0.63  # BW rewrite match successes           : 22
% 0.68/0.63  # Condensation attempts                : 118
% 0.68/0.63  # Condensation successes               : 16
% 0.68/0.63  # Termbank termtop insertions          : 249142
% 0.68/0.63  # Search garbage collected termcells   : 210
% 0.68/0.63  
% 0.68/0.63  # -------------------------------------------------
% 0.68/0.63  # User time                : 0.114 s
% 0.68/0.63  # System time              : 0.012 s
% 0.68/0.63  # Total time               : 0.126 s
% 0.68/0.63  # Maximum resident set size: 1832 pages
% 0.68/0.63  
% 0.68/0.63  # -------------------------------------------------
% 0.68/0.63  # User time                : 0.556 s
% 0.68/0.63  # System time              : 0.048 s
% 0.68/0.63  # Total time               : 0.604 s
% 0.68/0.63  # Maximum resident set size: 1720 pages
% 0.68/0.63  % E---3.1 exiting
% 0.68/0.63  % E exiting
%------------------------------------------------------------------------------