TSTP Solution File: SEU504^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU504^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 03:27:48 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   17 (   6 unt;   6 typ;   0 def)
%            Number of atoms       :   32 (  17 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  110 (  12   ~;  11   |;  15   &;  53   @)
%                                         (   2 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (   5   ^  21   !;  11   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    exu: ( $i > $o ) > $o ).

thf(decl_23,type,
    exuE1: $o ).

thf(decl_24,type,
    esk1_2: ( $i > $o ) > $i > $i ).

thf(decl_25,type,
    esk2_1: ( $i > $o ) > $i ).

thf(decl_26,type,
    epred1_0: $i > $o ).

thf(decl_27,type,
    esk3_0: $i ).

thf(exuE1,axiom,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).

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

thf(exuE3e,conjecture,
    ( exuE1
   => ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).

thf(c_0_3,plain,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE1]) ).

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

thf(c_0_5,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X9: $i] :
              ( ( X1 @ X9 )
              & ! [X10: $i] :
                  ( ( X1 @ X10 )
                 => ( X9 = X10 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_6,negated_conjecture,
    ~ ( ! [X11: $i > $o] :
          ( ? [X12: $i] :
              ( ( X11 @ X12 )
              & ! [X13: $i] :
                  ( ( X11 @ X13 )
                 => ( X12 = X13 ) ) )
         => ? [X14: $i] :
              ( ( X11 @ X14 )
              & ! [X15: $i] :
                  ( ( X11 @ X15 )
                 => ( X14 = X15 ) ) ) )
     => ! [X1: $i > $o] :
          ( ? [X16: $i] :
              ( ( X1 @ X16 )
              & ! [X17: $i] :
                  ( ( X1 @ X17 )
                 => ( X16 = X17 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[exuE3e])]),c_0_4]),c_0_5]) ).

thf(c_0_7,negated_conjecture,
    ! [X18: $i > $o,X19: $i,X22: $i,X25: $i,X26: $i] :
      ( ( ( X18 @ ( esk2_1 @ X18 ) )
        | ( X18 @ ( esk1_2 @ X18 @ X19 ) )
        | ~ ( X18 @ X19 ) )
      & ( ~ ( X18 @ X22 )
        | ( ( esk2_1 @ X18 )
          = X22 )
        | ( X18 @ ( esk1_2 @ X18 @ X19 ) )
        | ~ ( X18 @ X19 ) )
      & ( ( X18 @ ( esk2_1 @ X18 ) )
        | ( X19
         != ( esk1_2 @ X18 @ X19 ) )
        | ~ ( X18 @ X19 ) )
      & ( ~ ( X18 @ X22 )
        | ( ( esk2_1 @ X18 )
          = X22 )
        | ( X19
         != ( esk1_2 @ X18 @ X19 ) )
        | ~ ( X18 @ X19 ) )
      & ( epred1_0 @ esk3_0 )
      & ( ~ ( epred1_0 @ X25 )
        | ( esk3_0 = X25 ) )
      & ~ ( epred1_0 @ X26 ) ),
    inference(distribute,[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,
    epred1_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X2: $i] :
      ~ ( epred1_0 @ X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_8,c_0_9]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08  % Problem    : SEU504^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.09  % Command    : run_E %s %d THM
% 0.09/0.28  % Computer : n013.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit   : 300
% 0.09/0.28  % WCLimit    : 300
% 0.09/0.28  % DateTime   : Sun May 19 17:57:23 EDT 2024
% 0.09/0.28  % CPUTime    : 
% 0.13/0.37  Running higher-order theorem proving
% 0.13/0.37  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
% 0.13/0.38  # Version: 3.1.0-ho
% 0.13/0.38  # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.13/0.38  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.38  # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.38  # Starting sh5l with 300s (1) cores
% 0.13/0.38  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.38  # Starting new_bool_2 with 300s (1) cores
% 0.13/0.38  # new_bool_2 with pid 1532 completed with status 0
% 0.13/0.38  # Result found by new_bool_2
% 0.13/0.38  # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.13/0.38  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.38  # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.38  # Starting sh5l with 300s (1) cores
% 0.13/0.38  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.38  # Starting new_bool_2 with 300s (1) cores
% 0.13/0.38  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.38  # Search class: HGUSF-FFSF21-SHSFMMBN
% 0.13/0.38  # partial match(1): HGHSF-FFSF21-SHSFMMBN
% 0.13/0.38  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.38  # Starting new_ho_10 with 181s (1) cores
% 0.13/0.38  # new_ho_10 with pid 1535 completed with status 0
% 0.13/0.38  # Result found by new_ho_10
% 0.13/0.38  # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.13/0.38  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.38  # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.38  # Starting sh5l with 300s (1) cores
% 0.13/0.38  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.38  # Starting new_bool_2 with 300s (1) cores
% 0.13/0.38  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.38  # Search class: HGUSF-FFSF21-SHSFMMBN
% 0.13/0.38  # partial match(1): HGHSF-FFSF21-SHSFMMBN
% 0.13/0.38  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.38  # Starting new_ho_10 with 181s (1) cores
% 0.13/0.38  # Preprocessing time       : 0.001 s
% 0.13/0.38  # Presaturation interreduction done
% 0.13/0.38  
% 0.13/0.38  # Proof found!
% 0.13/0.38  # SZS status Theorem
% 0.13/0.38  # SZS output start CNFRefutation
% See solution above
% 0.13/0.38  # Parsed axioms                        : 5
% 0.13/0.38  # Removed by relevancy pruning/SinE    : 2
% 0.13/0.38  # Initial clauses                      : 7
% 0.13/0.38  # Removed in clause preprocessing      : 0
% 0.13/0.38  # Initial clauses in saturation        : 7
% 0.13/0.38  # Processed clauses                    : 2
% 0.13/0.38  # ...of these trivial                  : 0
% 0.13/0.38  # ...subsumed                          : 0
% 0.13/0.38  # ...remaining for further processing  : 2
% 0.13/0.38  # Other redundant clauses eliminated   : 0
% 0.13/0.38  # Clauses deleted for lack of memory   : 0
% 0.13/0.38  # Backward-subsumed                    : 0
% 0.13/0.38  # Backward-rewritten                   : 0
% 0.13/0.38  # Generated clauses                    : 1
% 0.13/0.38  # ...of the previous two non-redundant : 0
% 0.13/0.38  # ...aggressively subsumed             : 0
% 0.13/0.38  # Contextual simplify-reflections      : 0
% 0.13/0.38  # Paramodulations                      : 0
% 0.13/0.38  # Factorizations                       : 0
% 0.13/0.38  # NegExts                              : 0
% 0.13/0.38  # Equation resolutions                 : 0
% 0.13/0.38  # Disequality decompositions           : 0
% 0.13/0.38  # Total rewrite steps                  : 0
% 0.13/0.38  # ...of those cached                   : 0
% 0.13/0.38  # Propositional unsat checks           : 0
% 0.13/0.38  #    Propositional check models        : 0
% 0.13/0.38  #    Propositional check unsatisfiable : 0
% 0.13/0.38  #    Propositional clauses             : 0
% 0.13/0.38  #    Propositional clauses after purity: 0
% 0.13/0.38  #    Propositional unsat core size     : 0
% 0.13/0.38  #    Propositional preprocessing time  : 0.000
% 0.13/0.38  #    Propositional encoding time       : 0.000
% 0.13/0.38  #    Propositional solver time         : 0.000
% 0.13/0.38  #    Success case prop preproc time    : 0.000
% 0.13/0.38  #    Success case prop encoding time   : 0.000
% 0.13/0.38  #    Success case prop solver time     : 0.000
% 0.13/0.38  # Current number of processed clauses  : 1
% 0.13/0.38  #    Positive orientable unit clauses  : 0
% 0.13/0.38  #    Positive unorientable unit clauses: 0
% 0.13/0.38  #    Negative unit clauses             : 1
% 0.13/0.38  #    Non-unit-clauses                  : 0
% 0.13/0.38  # Current number of unprocessed clauses: 5
% 0.13/0.38  # ...number of literals in the above   : 16
% 0.13/0.38  # Current number of archived formulas  : 0
% 0.13/0.38  # Current number of archived clauses   : 1
% 0.13/0.38  # Clause-clause subsumption calls (NU) : 0
% 0.13/0.38  # Rec. Clause-clause subsumption calls : 0
% 0.13/0.38  # Non-unit clause-clause subsumptions  : 0
% 0.13/0.38  # Unit Clause-clause subsumption calls : 0
% 0.13/0.38  # Rewrite failures with RHS unbound    : 0
% 0.13/0.38  # BW rewrite match attempts            : 0
% 0.13/0.38  # BW rewrite match successes           : 0
% 0.13/0.38  # Condensation attempts                : 2
% 0.13/0.38  # Condensation successes               : 0
% 0.13/0.38  # Termbank termtop insertions          : 656
% 0.13/0.38  # Search garbage collected termcells   : 294
% 0.13/0.38  
% 0.13/0.38  # -------------------------------------------------
% 0.13/0.38  # User time                : 0.003 s
% 0.13/0.38  # System time              : 0.000 s
% 0.13/0.38  # Total time               : 0.003 s
% 0.13/0.38  # Maximum resident set size: 1764 pages
% 0.13/0.38  
% 0.13/0.38  # -------------------------------------------------
% 0.13/0.38  # User time                : 0.003 s
% 0.13/0.38  # System time              : 0.002 s
% 0.13/0.38  # Total time               : 0.005 s
% 0.13/0.38  # Maximum resident set size: 1712 pages
% 0.13/0.38  % E---3.1 exiting
% 0.13/0.38  % E exiting
%------------------------------------------------------------------------------