TSTP Solution File: SEU930^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 03:30:53 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   13 (   6 unt;   3 typ;   0 def)
%            Number of atoms       :   23 (  22 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   53 (   5   ~;   2   |;   5   &;  35   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   15 (   8   ^   7   !;   0   ?;  15   :)

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

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

thf(decl_24,type,
    esk1_0: $i ).

thf(cTHM171A_pme,conjecture,
    ( ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
      = ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) )
   => ! [X1: $i] :
        ( ( ( ( g @ X1 )
            = X1 )
          & ! [X2: $i] :
              ( ( ( g @ X2 )
                = X2 )
             => ( X2 = X1 ) ) )
       => ( ( f @ X1 )
          = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM171A_pme) ).

thf(c_0_1,negated_conjecture,
    ~ ( ( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
        = ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) )
     => ! [X1: $i] :
          ( ( ( ( g @ X1 )
              = X1 )
            & ! [X2: $i] :
                ( ( ( g @ X2 )
                  = X2 )
               => ( X2 = X1 ) ) )
         => ( ( f @ X1 )
            = X1 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM171A_pme])]) ).

thf(c_0_2,negated_conjecture,
    ! [X6: $i] :
      ( ( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
        = ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) )
      & ( ( g @ esk1_0 )
        = esk1_0 )
      & ( ( ( g @ X6 )
         != X6 )
        | ( X6 = esk1_0 ) )
      & ( ( f @ esk1_0 )
       != esk1_0 ) ),
    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,
    ( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
    = ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X1: $i] :
      ( ( f @ ( g @ X1 ) )
      = ( g @ ( f @ X1 ) ) ),
    inference(arg_cong,[status(thm)],[c_0_3]) ).

thf(c_0_5,negated_conjecture,
    ( ( g @ esk1_0 )
    = esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i] :
      ( ( X1 = esk1_0 )
      | ( ( g @ X1 )
       != X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,negated_conjecture,
    ( ( g @ ( f @ esk1_0 ) )
    = ( f @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ( ( f @ esk1_0 )
   != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_9,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n014.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Sun May 19 15:23:53 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  Running higher-order theorem proving
% 0.14/0.39  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
% 0.14/0.40  # Version: 3.1.0-ho
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.14/0.40  # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.40  # Starting new_bool_9 with 300s (1) cores
% 0.14/0.40  # Starting sh5l with 300s (1) cores
% 0.14/0.40  # new_bool_9 with pid 1506 completed with status 0
% 0.14/0.40  # Result found by new_bool_9
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.14/0.40  # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.40  # Starting new_bool_9 with 300s (1) cores
% 0.14/0.40  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.14/0.40  # Search class: HHUPF-FFSF11-MSSFFFNN
% 0.14/0.40  # partial match(1): HHUPF-FFSF11-MSSFFMNN
% 0.14/0.40  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.40  # Starting ho_unfolding_3 with 181s (1) cores
% 0.14/0.40  # ho_unfolding_3 with pid 1508 completed with status 0
% 0.14/0.40  # Result found by ho_unfolding_3
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.14/0.40  # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.40  # Starting new_bool_9 with 300s (1) cores
% 0.14/0.40  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.14/0.40  # Search class: HHUPF-FFSF11-MSSFFFNN
% 0.14/0.40  # partial match(1): HHUPF-FFSF11-MSSFFMNN
% 0.14/0.40  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.40  # Starting ho_unfolding_3 with 181s (1) cores
% 0.14/0.40  # Preprocessing time       : 0.001 s
% 0.14/0.40  # Presaturation interreduction done
% 0.14/0.40  
% 0.14/0.40  # Proof found!
% 0.14/0.40  # SZS status Theorem
% 0.14/0.40  # SZS output start CNFRefutation
% See solution above
% 0.14/0.40  # Parsed axioms                        : 3
% 0.14/0.40  # Removed by relevancy pruning/SinE    : 2
% 0.14/0.40  # Initial clauses                      : 4
% 0.14/0.40  # Removed in clause preprocessing      : 0
% 0.14/0.40  # Initial clauses in saturation        : 4
% 0.14/0.40  # Processed clauses                    : 10
% 0.14/0.40  # ...of these trivial                  : 0
% 0.14/0.40  # ...subsumed                          : 0
% 0.14/0.40  # ...remaining for further processing  : 10
% 0.14/0.40  # Other redundant clauses eliminated   : 0
% 0.14/0.40  # Clauses deleted for lack of memory   : 0
% 0.14/0.40  # Backward-subsumed                    : 0
% 0.14/0.40  # Backward-rewritten                   : 0
% 0.14/0.40  # Generated clauses                    : 4
% 0.14/0.40  # ...of the previous two non-redundant : 3
% 0.14/0.40  # ...aggressively subsumed             : 0
% 0.14/0.40  # Contextual simplify-reflections      : 0
% 0.14/0.40  # Paramodulations                      : 3
% 0.14/0.40  # Factorizations                       : 0
% 0.14/0.40  # NegExts                              : 0
% 0.14/0.40  # Equation resolutions                 : 0
% 0.14/0.40  # Disequality decompositions           : 0
% 0.14/0.40  # Total rewrite steps                  : 0
% 0.14/0.40  # ...of those cached                   : 0
% 0.14/0.40  # Propositional unsat checks           : 0
% 0.14/0.40  #    Propositional check models        : 0
% 0.14/0.40  #    Propositional check unsatisfiable : 0
% 0.14/0.40  #    Propositional clauses             : 0
% 0.14/0.40  #    Propositional clauses after purity: 0
% 0.14/0.40  #    Propositional unsat core size     : 0
% 0.14/0.40  #    Propositional preprocessing time  : 0.000
% 0.14/0.40  #    Propositional encoding time       : 0.000
% 0.14/0.40  #    Propositional solver time         : 0.000
% 0.14/0.40  #    Success case prop preproc time    : 0.000
% 0.14/0.40  #    Success case prop encoding time   : 0.000
% 0.14/0.40  #    Success case prop solver time     : 0.000
% 0.14/0.40  # Current number of processed clauses  : 6
% 0.14/0.40  #    Positive orientable unit clauses  : 4
% 0.14/0.40  #    Positive unorientable unit clauses: 0
% 0.14/0.40  #    Negative unit clauses             : 1
% 0.14/0.40  #    Non-unit-clauses                  : 1
% 0.14/0.40  # Current number of unprocessed clauses: 0
% 0.14/0.40  # ...number of literals in the above   : 0
% 0.14/0.40  # Current number of archived formulas  : 0
% 0.14/0.40  # Current number of archived clauses   : 4
% 0.14/0.40  # Clause-clause subsumption calls (NU) : 0
% 0.14/0.40  # Rec. Clause-clause subsumption calls : 0
% 0.14/0.40  # Non-unit clause-clause subsumptions  : 0
% 0.14/0.40  # Unit Clause-clause subsumption calls : 0
% 0.14/0.40  # Rewrite failures with RHS unbound    : 0
% 0.14/0.40  # BW rewrite match attempts            : 0
% 0.14/0.40  # BW rewrite match successes           : 0
% 0.14/0.40  # Condensation attempts                : 10
% 0.14/0.40  # Condensation successes               : 0
% 0.14/0.40  # Termbank termtop insertions          : 279
% 0.14/0.40  # Search garbage collected termcells   : 90
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.001 s
% 0.14/0.40  # System time              : 0.002 s
% 0.14/0.40  # Total time               : 0.003 s
% 0.14/0.40  # Maximum resident set size: 1796 pages
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.002 s
% 0.14/0.40  # System time              : 0.003 s
% 0.14/0.40  # Total time               : 0.005 s
% 0.14/0.40  # Maximum resident set size: 1700 pages
% 0.14/0.40  % E---3.1 exiting
% 0.14/0.40  % E exiting
%------------------------------------------------------------------------------