TSTP Solution File: SEU706^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 03:29:19 EDT 2024

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   32 (   9 unt;  13 typ;   0 def)
%            Number of atoms       :   80 (  45 equ;   0 cnn)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  169 (  16   ~;  12   |;  12   &;  96   @)
%                                         (   7 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :   52 (   2   ^  47   !;   3   ?;  52   :)

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

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

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

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

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

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

thf(decl_28,type,
    setadjoin__Cong: $o ).

thf(decl_29,type,
    setunion__Cong: $o ).

thf(decl_30,type,
    setunionsingleton: $o ).

thf(decl_31,type,
    singleton: $i > $o ).

thf(decl_32,type,
    esk1_0: $i ).

thf(decl_33,type,
    esk2_0: $i ).

thf(decl_34,type,
    esk3_0: $i ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [X3: $i] :
        ? [X1: $i] :
          ( ( in @ X1 @ X3 )
          & ( X3
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).

thf(theeq,conjecture,
    ( uniqinunit
   => ( in__Cong
     => ( setadjoin__Cong
       => ( setunion__Cong
         => ( setunionsingleton
           => ! [X7: $i] :
                ( ( singleton @ X7 )
               => ! [X1: $i] :
                    ( ( in @ X1 @ X7 )
                   => ( ( setunion @ X7 )
                      = X1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).

thf(setunion__Cong,axiom,
    ( setunion__Cong
  <=> ! [X3: $i,X4: $i] :
        ( ( X3 = X4 )
       => ( ( setunion @ X3 )
          = ( setunion @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).

thf(in__Cong,axiom,
    ( in__Cong
  <=> ! [X3: $i,X4: $i] :
        ( ( X3 = X4 )
       => ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( in @ X1 @ X3 )
            <=> ( in @ X2 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).

thf(setunionsingleton,axiom,
    ( setunionsingleton
  <=> ! [X1: $i] :
        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
        = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).

thf(setadjoin__Cong,axiom,
    ( setadjoin__Cong
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ! [X5: $i,X6: $i] :
            ( ( X5 = X6 )
           => ( ( setadjoin @ X1 @ X5 )
              = ( setadjoin @ X2 @ X6 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(c_0_7,plain,
    ( singleton
    = ( ^ [Z0: $i] :
        ? [X1: $i] :
          ( ( in @ X1 @ Z0 )
          & ( Z0
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singleton]) ).

thf(c_0_8,negated_conjecture,
    ~ ( ! [X23: $i,X24: $i] :
          ( ( in @ X23 @ ( setadjoin @ X24 @ emptyset ) )
         => ( X23 = X24 ) )
     => ( ! [X25: $i,X26: $i] :
            ( ( X25 = X26 )
           => ! [X27: $i,X28: $i] :
                ( ( X27 = X28 )
               => ( ( in @ X27 @ X25 )
                <=> ( in @ X28 @ X26 ) ) ) )
       => ( ! [X29: $i,X30: $i] :
              ( ( X29 = X30 )
             => ! [X31: $i,X32: $i] :
                  ( ( X31 = X32 )
                 => ( ( setadjoin @ X29 @ X31 )
                    = ( setadjoin @ X30 @ X32 ) ) ) )
         => ( ! [X33: $i,X34: $i] :
                ( ( X33 = X34 )
               => ( ( setunion @ X33 )
                  = ( setunion @ X34 ) ) )
           => ( ! [X35: $i] :
                  ( ( setunion @ ( setadjoin @ X35 @ emptyset ) )
                  = X35 )
             => ! [X7: $i] :
                  ( ? [X36: $i] :
                      ( ( in @ X36 @ X7 )
                      & ( X7
                        = ( setadjoin @ X36 @ emptyset ) ) )
                 => ! [X1: $i] :
                      ( ( in @ X1 @ X7 )
                     => ( ( setunion @ X7 )
                        = X1 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[theeq]),setunion__Cong]),c_0_7]),in__Cong]),uniqinunit]),setunionsingleton]),setadjoin__Cong]) ).

thf(c_0_9,negated_conjecture,
    ! [X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
      ( ( ~ ( in @ X37 @ ( setadjoin @ X38 @ emptyset ) )
        | ( X37 = X38 ) )
      & ( ~ ( in @ X41 @ X39 )
        | ( in @ X42 @ X40 )
        | ( X41 != X42 )
        | ( X39 != X40 ) )
      & ( ~ ( in @ X42 @ X40 )
        | ( in @ X41 @ X39 )
        | ( X41 != X42 )
        | ( X39 != X40 ) )
      & ( ( X43 != X44 )
        | ( X45 != X46 )
        | ( ( setadjoin @ X43 @ X45 )
          = ( setadjoin @ X44 @ X46 ) ) )
      & ( ( X47 != X48 )
        | ( ( setunion @ X47 )
          = ( setunion @ X48 ) ) )
      & ( ( setunion @ ( setadjoin @ X49 @ emptyset ) )
        = X49 )
      & ( in @ esk2_0 @ esk1_0 )
      & ( esk1_0
        = ( setadjoin @ esk2_0 @ emptyset ) )
      & ( in @ esk3_0 @ esk1_0 )
      & ( ( setunion @ esk1_0 )
       != esk3_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_8])])])])])]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ( esk1_0
    = ( setadjoin @ esk2_0 @ emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

thf(c_0_13,negated_conjecture,
    in @ esk3_0 @ esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,negated_conjecture,
    ( ( setunion @ esk1_0 )
   != esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_15,negated_conjecture,
    esk3_0 = esk2_0,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i] :
      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_17,negated_conjecture,
    ( ( setunion @ esk1_0 )
   != esk2_0 ),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_18,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem    : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.07  % Command    : run_E %s %d THM
% 0.07/0.28  % Computer : n021.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit   : 300
% 0.07/0.28  % WCLimit    : 300
% 0.07/0.28  % DateTime   : Sun May 19 17:37:22 EDT 2024
% 0.07/0.28  % CPUTime    : 
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  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
% 0.12/0.36  # Version: 3.1.0-ho
% 0.12/0.36  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36  # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36  # Starting lpo1_def_fix with 300s (1) cores
% 0.12/0.36  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.12/0.36  # ehoh_best_sine_rwall with pid 14426 completed with status 0
% 0.12/0.36  # Result found by ehoh_best_sine_rwall
% 0.12/0.36  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36  # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.36  # Search class: HHUSF-FFSS21-SSFFMFNN
% 0.12/0.36  # partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.12/0.36  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.36  # Starting new_ho_10 with 163s (1) cores
% 0.12/0.36  # new_ho_10 with pid 14429 completed with status 0
% 0.12/0.36  # Result found by new_ho_10
% 0.12/0.36  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36  # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.36  # Search class: HHUSF-FFSS21-SSFFMFNN
% 0.12/0.36  # partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.12/0.36  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.36  # Starting new_ho_10 with 163s (1) cores
% 0.12/0.36  # Preprocessing time       : 0.001 s
% 0.12/0.36  # Presaturation interreduction done
% 0.12/0.36  
% 0.12/0.36  # Proof found!
% 0.12/0.36  # SZS status Theorem
% 0.12/0.36  # SZS output start CNFRefutation
% See solution above
% 0.12/0.36  # Parsed axioms                        : 17
% 0.12/0.36  # Removed by relevancy pruning/SinE    : 10
% 0.12/0.36  # Initial clauses                      : 10
% 0.12/0.36  # Removed in clause preprocessing      : 4
% 0.12/0.36  # Initial clauses in saturation        : 6
% 0.12/0.36  # Processed clauses                    : 15
% 0.12/0.36  # ...of these trivial                  : 0
% 0.12/0.36  # ...subsumed                          : 0
% 0.12/0.36  # ...remaining for further processing  : 15
% 0.12/0.36  # Other redundant clauses eliminated   : 0
% 0.12/0.36  # Clauses deleted for lack of memory   : 0
% 0.12/0.36  # Backward-subsumed                    : 0
% 0.12/0.36  # Backward-rewritten                   : 2
% 0.12/0.36  # Generated clauses                    : 3
% 0.12/0.36  # ...of the previous two non-redundant : 3
% 0.12/0.36  # ...aggressively subsumed             : 0
% 0.12/0.36  # Contextual simplify-reflections      : 0
% 0.12/0.36  # Paramodulations                      : 3
% 0.12/0.36  # Factorizations                       : 0
% 0.12/0.36  # NegExts                              : 0
% 0.12/0.36  # Equation resolutions                 : 0
% 0.12/0.36  # Disequality decompositions           : 0
% 0.12/0.36  # Total rewrite steps                  : 3
% 0.12/0.36  # ...of those cached                   : 1
% 0.12/0.36  # Propositional unsat checks           : 0
% 0.12/0.36  #    Propositional check models        : 0
% 0.12/0.36  #    Propositional check unsatisfiable : 0
% 0.12/0.36  #    Propositional clauses             : 0
% 0.12/0.36  #    Propositional clauses after purity: 0
% 0.12/0.36  #    Propositional unsat core size     : 0
% 0.12/0.36  #    Propositional preprocessing time  : 0.000
% 0.12/0.36  #    Propositional encoding time       : 0.000
% 0.12/0.36  #    Propositional solver time         : 0.000
% 0.12/0.36  #    Success case prop preproc time    : 0.000
% 0.12/0.36  #    Success case prop encoding time   : 0.000
% 0.12/0.36  #    Success case prop solver time     : 0.000
% 0.12/0.36  # Current number of processed clauses  : 7
% 0.12/0.36  #    Positive orientable unit clauses  : 4
% 0.12/0.36  #    Positive unorientable unit clauses: 0
% 0.12/0.36  #    Negative unit clauses             : 1
% 0.12/0.36  #    Non-unit-clauses                  : 2
% 0.12/0.36  # Current number of unprocessed clauses: 0
% 0.12/0.36  # ...number of literals in the above   : 0
% 0.12/0.36  # Current number of archived formulas  : 0
% 0.12/0.36  # Current number of archived clauses   : 8
% 0.12/0.36  # Clause-clause subsumption calls (NU) : 0
% 0.12/0.36  # Rec. Clause-clause subsumption calls : 0
% 0.12/0.36  # Non-unit clause-clause subsumptions  : 0
% 0.12/0.36  # Unit Clause-clause subsumption calls : 0
% 0.12/0.36  # Rewrite failures with RHS unbound    : 0
% 0.12/0.36  # BW rewrite match attempts            : 1
% 0.12/0.36  # BW rewrite match successes           : 1
% 0.12/0.36  # Condensation attempts                : 15
% 0.12/0.36  # Condensation successes               : 0
% 0.12/0.36  # Termbank termtop insertions          : 1063
% 0.12/0.36  # Search garbage collected termcells   : 439
% 0.12/0.36  
% 0.12/0.36  # -------------------------------------------------
% 0.12/0.36  # User time                : 0.001 s
% 0.12/0.36  # System time              : 0.002 s
% 0.12/0.36  # Total time               : 0.003 s
% 0.12/0.36  # Maximum resident set size: 1912 pages
% 0.12/0.36  
% 0.12/0.36  # -------------------------------------------------
% 0.12/0.36  # User time                : 0.001 s
% 0.12/0.36  # System time              : 0.004 s
% 0.12/0.36  # Total time               : 0.005 s
% 0.12/0.36  # Maximum resident set size: 1708 pages
% 0.12/0.36  % E---3.1 exiting
% 0.12/0.37  % E exiting
%------------------------------------------------------------------------------