TSTP Solution File: SET753^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% 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 02:55:32 EDT 2024

% Result   : Theorem 0.15s 0.41s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   40 (  18 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   80 (  11   ~;   7   |;  12   &;  47   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   35 (  16   ^  14   !;   5   ?;  35   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_29,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_33,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

thf(decl_36,type,
    fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

thf(decl_44,type,
    epred1_0: $i > $o ).

thf(decl_45,type,
    epred2_0: $i > $o ).

thf(decl_46,type,
    esk1_0: $i > $i ).

thf(decl_47,type,
    esk2_0: $i ).

thf(decl_48,type,
    esk3_0: $i ).

thf(intersection,axiom,
    ( intersection
    = ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
          ( ( X9 @ X4 )
          & ( X10 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).

thf(subset,axiom,
    ( subset
    = ( ^ [X16: $i > $o,X17: $i > $o] :
        ! [X4: $i] :
          ( ( X16 @ X4 )
         => ( X17 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',subset) ).

thf(fun_image,axiom,
    ( fun_image
    = ( ^ [X22: $i > $i,X23: $i > $o,X3: $i] :
        ? [X1: $i] :
          ( ( X23 @ X1 )
          & ( X3
            = ( X22 @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_image) ).

thf(thm,conjecture,
    ! [X27: $i > $o,X28: $i > $o,X22: $i > $i] : ( subset @ ( fun_image @ X22 @ ( intersection @ X27 @ X28 ) ) @ ( intersection @ ( fun_image @ X22 @ X27 ) @ ( fun_image @ X22 @ X28 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(c_0_4,plain,
    ( intersection
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[intersection]) ).

thf(c_0_5,plain,
    ( subset
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subset]) ).

thf(c_0_6,plain,
    ( fun_image
    = ( ^ [Z0: $i > $i,Z1: $i > $o,Z2: $i] :
        ? [X1: $i] :
          ( ( Z1 @ X1 )
          & ( Z2
            = ( Z0 @ X1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fun_image]) ).

thf(c_0_7,negated_conjecture,
    ~ ! [X27: $i > $o,X28: $i > $o,X22: $i > $i,X39: $i] :
        ( ? [X36: $i] :
            ( ( X27 @ X36 )
            & ( X28 @ X36 )
            & ( X39
              = ( X22 @ X36 ) ) )
       => ( ? [X37: $i] :
              ( ( X27 @ X37 )
              & ( X39
                = ( X22 @ X37 ) ) )
          & ? [X38: $i] :
              ( ( X28 @ X38 )
              & ( X39
                = ( X22 @ X38 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_4]),c_0_5]),c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X51: $i,X52: $i] :
      ( ( epred1_0 @ esk3_0 )
      & ( epred2_0 @ esk3_0 )
      & ( esk2_0
        = ( esk1_0 @ esk3_0 ) )
      & ( ~ ( epred1_0 @ X51 )
        | ( esk2_0
         != ( esk1_0 @ X51 ) )
        | ~ ( epred2_0 @ X52 )
        | ( esk2_0
         != ( esk1_0 @ X52 ) ) ) ),
    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_7])])])])]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ~ ( epred1_0 @ X1 )
      | ( esk2_0
       != ( esk1_0 @ X1 ) )
      | ~ ( epred2_0 @ X3 )
      | ( esk2_0
       != ( esk1_0 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_10,negated_conjecture,
    epred1_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ( esk2_0
    = ( esk1_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: $i] :
      ( ( ( esk1_0 @ X1 )
       != esk2_0 )
      | ~ ( epred2_0 @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).

thf(c_0_13,negated_conjecture,
    epred2_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.09/0.30  % Computer : n023.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon May 20 13:10:37 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.15/0.40  Running higher-order theorem proving
% 0.15/0.40  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
% 0.15/0.41  # Version: 3.1.0-ho
% 0.15/0.41  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41  # Starting sh1l with 300s (1) cores
% 0.15/0.41  # Starting post_as_ho10 with 300s (1) cores
% 0.15/0.41  # post_as_ho1 with pid 24464 completed with status 0
% 0.15/0.41  # Result found by post_as_ho1
% 0.15/0.41  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41  # No SInE strategy applied
% 0.15/0.41  # Search class: HUHSF-FFSS33-SHSSMSNN
% 0.15/0.41  # partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.15/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41  # new_ho_10 with pid 24467 completed with status 0
% 0.15/0.41  # Result found by new_ho_10
% 0.15/0.41  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41  # No SInE strategy applied
% 0.15/0.41  # Search class: HUHSF-FFSS33-SHSSMSNN
% 0.15/0.41  # partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.15/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41  # Preprocessing time       : 0.001 s
% 0.15/0.41  # Presaturation interreduction done
% 0.15/0.41  
% 0.15/0.41  # Proof found!
% 0.15/0.41  # SZS status Theorem
% 0.15/0.41  # SZS output start CNFRefutation
% See solution above
% 0.15/0.41  # Parsed axioms                        : 45
% 0.15/0.41  # Removed by relevancy pruning/SinE    : 0
% 0.15/0.41  # Initial clauses                      : 27
% 0.15/0.41  # Removed in clause preprocessing      : 22
% 0.15/0.41  # Initial clauses in saturation        : 5
% 0.15/0.41  # Processed clauses                    : 11
% 0.15/0.41  # ...of these trivial                  : 0
% 0.15/0.41  # ...subsumed                          : 0
% 0.15/0.41  # ...remaining for further processing  : 11
% 0.15/0.41  # Other redundant clauses eliminated   : 0
% 0.15/0.41  # Clauses deleted for lack of memory   : 0
% 0.15/0.41  # Backward-subsumed                    : 1
% 0.15/0.41  # Backward-rewritten                   : 0
% 0.15/0.41  # Generated clauses                    : 2
% 0.15/0.41  # ...of the previous two non-redundant : 1
% 0.15/0.41  # ...aggressively subsumed             : 0
% 0.15/0.41  # Contextual simplify-reflections      : 0
% 0.15/0.41  # Paramodulations                      : 2
% 0.15/0.41  # Factorizations                       : 0
% 0.15/0.41  # NegExts                              : 0
% 0.15/0.41  # Equation resolutions                 : 0
% 0.15/0.41  # Disequality decompositions           : 0
% 0.15/0.41  # Total rewrite steps                  : 2
% 0.15/0.41  # ...of those cached                   : 1
% 0.15/0.41  # Propositional unsat checks           : 0
% 0.15/0.41  #    Propositional check models        : 0
% 0.15/0.41  #    Propositional check unsatisfiable : 0
% 0.15/0.41  #    Propositional clauses             : 0
% 0.15/0.41  #    Propositional clauses after purity: 0
% 0.15/0.41  #    Propositional unsat core size     : 0
% 0.15/0.41  #    Propositional preprocessing time  : 0.000
% 0.15/0.41  #    Propositional encoding time       : 0.000
% 0.15/0.41  #    Propositional solver time         : 0.000
% 0.15/0.41  #    Success case prop preproc time    : 0.000
% 0.15/0.41  #    Success case prop encoding time   : 0.000
% 0.15/0.41  #    Success case prop solver time     : 0.000
% 0.15/0.41  # Current number of processed clauses  : 5
% 0.15/0.41  #    Positive orientable unit clauses  : 4
% 0.15/0.41  #    Positive unorientable unit clauses: 0
% 0.15/0.41  #    Negative unit clauses             : 0
% 0.15/0.41  #    Non-unit-clauses                  : 1
% 0.15/0.41  # Current number of unprocessed clauses: 0
% 0.15/0.41  # ...number of literals in the above   : 0
% 0.15/0.41  # Current number of archived formulas  : 0
% 0.15/0.41  # Current number of archived clauses   : 6
% 0.15/0.41  # Clause-clause subsumption calls (NU) : 3
% 0.15/0.41  # Rec. Clause-clause subsumption calls : 3
% 0.15/0.41  # Non-unit clause-clause subsumptions  : 1
% 0.15/0.41  # Unit Clause-clause subsumption calls : 0
% 0.15/0.41  # Rewrite failures with RHS unbound    : 0
% 0.15/0.41  # BW rewrite match attempts            : 0
% 0.15/0.41  # BW rewrite match successes           : 0
% 0.15/0.41  # Condensation attempts                : 11
% 0.15/0.41  # Condensation successes               : 0
% 0.15/0.41  # Termbank termtop insertions          : 1473
% 0.15/0.41  # Search garbage collected termcells   : 278
% 0.15/0.41  
% 0.15/0.41  # -------------------------------------------------
% 0.15/0.41  # User time                : 0.002 s
% 0.15/0.41  # System time              : 0.002 s
% 0.15/0.41  # Total time               : 0.004 s
% 0.15/0.41  # Maximum resident set size: 1872 pages
% 0.15/0.41  
% 0.15/0.41  # -------------------------------------------------
% 0.15/0.41  # User time                : 0.004 s
% 0.15/0.41  # System time              : 0.003 s
% 0.15/0.41  # Total time               : 0.007 s
% 0.15/0.41  # Maximum resident set size: 1780 pages
% 0.15/0.41  % E---3.1 exiting
% 0.15/0.41  % E exiting
%------------------------------------------------------------------------------