TSTP Solution File: SEU938^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU938^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 03:30:54 EDT 2024

% Result   : Theorem 0.21s 0.56s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   22 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :   42 (  28 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  272 (  31   ~;  34   |;  16   &; 177   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   64 (  64   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-4 aty)
%            Number of variables   :   69 (  30   ^  39   !;   0   ?;  69   :)

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

thf(decl_23,type,
    b: $i ).

thf(decl_24,type,
    h: $i > $i ).

thf(decl_25,type,
    esk1_2: ( $i > $i ) > ( $i > $i ) > $i ).

thf(decl_26,type,
    epred1_2: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).

thf(decl_27,type,
    esk2_3: ( $i > $i ) > ( $i > $i ) > ( ( $i > $i ) > $o ) > $i > $i ).

thf(cTHM196_pme,conjecture,
    ( ( ( ( h @ a )
        = a )
      & ( ( h @ b )
       != a )
      & ! [X1: $i > $i,X2: $i > $i] :
          ( ! [X3: $i] :
              ( ( X1 @ X3 )
              = ( X2 @ X3 ) )
         => ( X1 = X2 ) ) )
   => ~ ! [X4: $i > $i,X5: $i > $i] :
          ( ! [X6: ( $i > $i ) > $o] :
              ( ( ( X6 @ X4 )
                & ! [X7: $i > $i] :
                    ( ( X6 @ X7 )
                   => ( X6
                      @ ^ [X3: $i] : ( X4 @ ( X7 @ X3 ) ) ) ) )
             => ( X6
                @ ^ [X3: $i] : ( X5 @ ( X4 @ X3 ) ) ) )
         => ! [X6: ( $i > $i ) > $o] :
              ( ( ( X6 @ X4 )
                & ! [X8: $i > $i] :
                    ( ( X6 @ X8 )
                   => ( X6
                      @ ^ [X3: $i] : ( X4 @ ( X8 @ X3 ) ) ) ) )
             => ( X6 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196_pme) ).

thf(c_0_1,negated_conjecture,
    ~ ( ( ( ( h @ a )
          = a )
        & ( ( h @ b )
         != a )
        & ! [X1: $i > $i,X2: $i > $i] :
            ( ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X2 @ X3 ) )
           => ( X1 = X2 ) ) )
     => ~ ! [X4: $i > $i,X5: $i > $i] :
            ( ! [X6: ( $i > $i ) > $o] :
                ( ( ( X6 @ X4 )
                  & ! [X7: $i > $i] :
                      ( ( X6 @ X7 )
                     => ( X6
                        @ ^ [Z0: $i] : ( X4 @ ( X7 @ Z0 ) ) ) ) )
               => ( X6
                  @ ^ [Z0: $i] : ( X5 @ ( X4 @ Z0 ) ) ) )
           => ! [X6: ( $i > $i ) > $o] :
                ( ( ( X6 @ X4 )
                  & ! [X8: $i > $i] :
                      ( ( X6 @ X8 )
                     => ( X6
                        @ ^ [Z0: $i] : ( X4 @ ( X8 @ Z0 ) ) ) ) )
               => ( X6 @ X5 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM196_pme])])]) ).

thf(c_0_2,negated_conjecture,
    ! [X18: $i > $i,X19: $i > $i,X21: $i > $i,X22: $i > $i,X24: $i > $i,X25: ( $i > $i ) > $o] :
      ( ( ( h @ a )
        = a )
      & ( ( h @ b )
       != a )
      & ( ( ( X18 @ ( esk1_2 @ X18 @ X19 ) )
         != ( X19 @ ( esk1_2 @ X18 @ X19 ) ) )
        | ( X18 = X19 ) )
      & ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ( epred1_2 @ X21 @ X22 @ X21 ) )
      & ( ~ ( X25
            @ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ( epred1_2 @ X21 @ X22 @ X21 ) )
      & ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ~ ( epred1_2 @ X21 @ X22 @ X24 )
        | ( epred1_2 @ X21 @ X22
          @ ^ [Z0: $i] : ( X21 @ ( X24 @ Z0 ) ) ) )
      & ( ~ ( X25
            @ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ~ ( epred1_2 @ X21 @ X22 @ X24 )
        | ( epred1_2 @ X21 @ X22
          @ ^ [Z0: $i] : ( X21 @ ( X24 @ Z0 ) ) ) )
      & ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ~ ( epred1_2 @ X21 @ X22
            @ ^ [Z0: $i] : ( X22 @ ( X21 @ Z0 ) ) ) )
      & ( ~ ( X25
            @ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
        | ~ ( X25 @ X21 )
        | ( X25 @ X22 )
        | ~ ( epred1_2 @ X21 @ X22
            @ ^ [Z0: $i] : ( X22 @ ( X21 @ Z0 ) ) ) ) ),
    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_1])])])])])]) ).

thf(c_0_3,negated_conjecture,
    ! [X1: $i > $i,X2: $i > $i] :
      ( ( X1 = X2 )
      | ( ( X1 @ ( esk1_2 @ X1 @ X2 ) )
       != ( X2 @ ( esk1_2 @ X1 @ X2 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ( ( h @ a )
    = a ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_5,negated_conjecture,
    ! [X6: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
      ( ( X6 @ X2 )
      | ( epred1_2 @ X1 @ X2 @ X1 )
      | ~ ( X6
          @ ^ [Z0: $i] : ( X1 @ ( esk2_3 @ X1 @ X2 @ X6 @ Z0 ) ) )
      | ~ ( X6 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i > $i] :
      ( ( X1
        = ( ^ [Z0: $i] : ( h @ a ) ) )
      | ( ( X1
          @ ( esk1_2 @ X1
            @ ^ [Z0: $i] : ( h @ a ) ) )
       != a ) ),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_7,negated_conjecture,
    ! [X6: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
      ( ( X6 @ X2 )
      | ~ ( X6
          @ ^ [Z0: $i] : ( X1 @ ( esk2_3 @ X1 @ X2 @ X6 @ Z0 ) ) )
      | ~ ( X6 @ X1 )
      | ~ ( epred1_2 @ X1 @ X2
          @ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i > $i,X2: $i > $i] :
      ( ( X1 = X2 )
      | ( epred1_2 @ X2 @ X1 @ X2 )
      | ( ( ^ [Z0: $i] :
              ( X2
              @ ( esk2_3 @ X2 @ X1
                @ ^ [Z1: $i > $i] : ( Z1 = X2 )
                @ Z0 ) ) )
       != X2 ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_5]) ).

thf(c_0_9,negated_conjecture,
    ( ( ^ [Z0: $i] : ( h @ a ) )
    = ( ^ [Z0: $i] : a ) ),
    inference(er,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ! [X2: $i > $i,X1: $i > $i] :
      ( ( ( ^ [Z0: $i] :
              ( X1
              @ ( esk2_3 @ X1 @ X2
                @ ^ [Z1: $i > $i] : ( Z1 != X2 )
                @ Z0 ) ) )
        = X2 )
      | ( X1 = X2 )
      | ~ ( epred1_2 @ X1 @ X2
          @ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i > $i] :
      ( ( X1
        = ( ^ [Z0: $i] : a ) )
      | ( epred1_2
        @ ^ [Z0: $i] : a
        @ X1
        @ ^ [Z0: $i] : a ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9])]) ).

thf(c_0_12,negated_conjecture,
    ( ( ^ [Z0: $i] : Z0 )
    = ( ^ [Z0: $i] : a ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_13,negated_conjecture,
    ( ( h @ b )
   != a ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_14,negated_conjecture,
    ! [X3: $i] : ( X3 = a ),
    inference(arg_cong,[status(thm)],[c_0_12]) ).

thf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU938^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n010.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 15:35:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  Running higher-order theorem proving
% 0.21/0.51  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/benchmark/theBenchmark.p
% 0.21/0.56  # Version: 3.1.0-ho
% 0.21/0.56  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.56  # Starting sh2lt with 300s (1) cores
% 0.21/0.56  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.21/0.56  # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.56  # post_as_ho5 with pid 13872 completed with status 0
% 0.21/0.56  # Result found by post_as_ho5
% 0.21/0.56  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.56  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.21/0.56  # Search class: HGUSF-FFSF32-MHHFFMBN
% 0.21/0.56  # partial match(2): HGUNF-FFSF32-SHHFFMBN
% 0.21/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.56  # Starting ho_unfolding_3 with 811s (1) cores
% 0.21/0.56  # Starting post_as_ho5 with 151s (1) cores
% 0.21/0.56  # Starting sh5l with 136s (1) cores
% 0.21/0.56  # Starting new_bool_3 with 136s (1) cores
% 0.21/0.56  # Starting new_bool_2 with 136s (1) cores
% 0.21/0.56  # post_as_ho5 with pid 13877 completed with status 0
% 0.21/0.56  # Result found by post_as_ho5
% 0.21/0.56  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.56  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.21/0.56  # Search class: HGUSF-FFSF32-MHHFFMBN
% 0.21/0.56  # partial match(2): HGUNF-FFSF32-SHHFFMBN
% 0.21/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.56  # Starting ho_unfolding_3 with 811s (1) cores
% 0.21/0.56  # Starting post_as_ho5 with 151s (1) cores
% 0.21/0.56  # Preprocessing time       : 0.001 s
% 0.21/0.56  # Presaturation interreduction done
% 0.21/0.56  
% 0.21/0.56  # Proof found!
% 0.21/0.56  # SZS status Theorem
% 0.21/0.56  # SZS output start CNFRefutation
% See solution above
% 0.21/0.56  # Parsed axioms                        : 4
% 0.21/0.56  # Removed by relevancy pruning/SinE    : 3
% 0.21/0.56  # Initial clauses                      : 9
% 0.21/0.56  # Removed in clause preprocessing      : 0
% 0.21/0.56  # Initial clauses in saturation        : 9
% 0.21/0.56  # Processed clauses                    : 58
% 0.21/0.56  # ...of these trivial                  : 0
% 0.21/0.56  # ...subsumed                          : 15
% 0.21/0.56  # ...remaining for further processing  : 43
% 0.21/0.56  # Other redundant clauses eliminated   : 14
% 0.21/0.56  # Clauses deleted for lack of memory   : 0
% 0.21/0.56  # Backward-subsumed                    : 2
% 0.21/0.56  # Backward-rewritten                   : 15
% 0.21/0.56  # Generated clauses                    : 355
% 0.21/0.56  # ...of the previous two non-redundant : 307
% 0.21/0.56  # ...aggressively subsumed             : 0
% 0.21/0.56  # Contextual simplify-reflections      : 0
% 0.21/0.56  # Paramodulations                      : 279
% 0.21/0.56  # Factorizations                       : 2
% 0.21/0.56  # NegExts                              : 2
% 0.21/0.56  # Equation resolutions                 : 33
% 0.21/0.56  # Disequality decompositions           : 0
% 0.21/0.56  # Total rewrite steps                  : 61
% 0.21/0.56  # ...of those cached                   : 52
% 0.21/0.56  # Propositional unsat checks           : 0
% 0.21/0.56  #    Propositional check models        : 0
% 0.21/0.56  #    Propositional check unsatisfiable : 0
% 0.21/0.56  #    Propositional clauses             : 0
% 0.21/0.56  #    Propositional clauses after purity: 0
% 0.21/0.56  #    Propositional unsat core size     : 0
% 0.21/0.56  #    Propositional preprocessing time  : 0.000
% 0.21/0.56  #    Propositional encoding time       : 0.000
% 0.21/0.56  #    Propositional solver time         : 0.000
% 0.21/0.56  #    Success case prop preproc time    : 0.000
% 0.21/0.56  #    Success case prop encoding time   : 0.000
% 0.21/0.56  #    Success case prop solver time     : 0.000
% 0.21/0.56  # Current number of processed clauses  : 17
% 0.21/0.56  #    Positive orientable unit clauses  : 1
% 0.21/0.56  #    Positive unorientable unit clauses: 1
% 0.21/0.56  #    Negative unit clauses             : 0
% 0.21/0.56  #    Non-unit-clauses                  : 15
% 0.21/0.56  # Current number of unprocessed clauses: 267
% 0.21/0.56  # ...number of literals in the above   : 1009
% 0.21/0.56  # Current number of archived formulas  : 0
% 0.21/0.56  # Current number of archived clauses   : 26
% 0.21/0.56  # Clause-clause subsumption calls (NU) : 84
% 0.21/0.56  # Rec. Clause-clause subsumption calls : 46
% 0.21/0.56  # Non-unit clause-clause subsumptions  : 15
% 0.21/0.56  # Unit Clause-clause subsumption calls : 9
% 0.21/0.56  # Rewrite failures with RHS unbound    : 0
% 0.21/0.56  # BW rewrite match attempts            : 50
% 0.21/0.56  # BW rewrite match successes           : 17
% 0.21/0.56  # Condensation attempts                : 0
% 0.21/0.56  # Condensation successes               : 0
% 0.21/0.56  # Termbank termtop insertions          : 37284
% 0.21/0.56  # Search garbage collected termcells   : 377
% 0.21/0.56  
% 0.21/0.56  # -------------------------------------------------
% 0.21/0.56  # User time                : 0.029 s
% 0.21/0.56  # System time              : 0.003 s
% 0.21/0.56  # Total time               : 0.033 s
% 0.21/0.56  # Maximum resident set size: 1884 pages
% 0.21/0.56  
% 0.21/0.56  # -------------------------------------------------
% 0.21/0.56  # User time                : 0.136 s
% 0.21/0.56  # System time              : 0.008 s
% 0.21/0.56  # Total time               : 0.144 s
% 0.21/0.56  # Maximum resident set size: 1732 pages
% 0.21/0.56  % E---3.1 exiting
% 0.21/0.56  % E exiting
%------------------------------------------------------------------------------