TSTP Solution File: SEU620^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 03:28:37 EDT 2024

% Result   : Theorem 0.22s 0.50s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   32 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   50 (  19 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  444 (  12   ~;   7   |;  13   &; 409   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   51 (   4   ^  37   !;  10   ?;  51   :)

% 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,
    iskpair: $i > $o ).

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

thf(decl_28,type,
    kpair: $i > $i > $i ).

thf(decl_29,type,
    esk1_2: $i > $i > $i ).

thf(decl_30,type,
    esk2_2: $i > $i > $i ).

thf(decl_31,type,
    esk3_0: $i ).

thf(decl_32,type,
    esk4_0: $i ).

thf(iskpair,axiom,
    ( iskpair
    = ( ^ [X1: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ X1 ) )
              & ( X1
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).

thf(kpairiskpair,axiom,
    ( kpairiskpair
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).

thf(kpairp,conjecture,
    ( kpairiskpair
   => ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).

thf(kpair,axiom,
    ( kpair
    = ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).

thf(c_0_4,plain,
    ( iskpair
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ Z0 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ Z0 ) )
              & ( Z0
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iskpair]) ).

thf(c_0_5,axiom,
    ( kpairiskpair
    = ( ! [X2: $i,X3: $i] :
        ? [X8: $i] :
          ( ( in @ X8 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [X9: $i] :
              ( ( in @ X9 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X9 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[kpairiskpair,c_0_4]) ).

thf(c_0_6,negated_conjecture,
    ~ ( ! [X10: $i,X11: $i] :
        ? [X12: $i] :
          ( ( in @ X12 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [X13: $i] :
              ( ( in @ X13 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X13 @ emptyset ) ) @ emptyset ) ) ) ) )
     => ! [X2: $i,X3: $i] :
        ? [X14: $i] :
          ( ( in @ X14 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
          & ? [X15: $i] :
              ( ( in @ X15 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
              & ( ( kpair @ X2 @ X3 )
                = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X15 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[kpairp]),c_0_4]),c_0_5]) ).

thf(c_0_7,plain,
    ! [X16: $i,X17: $i] :
      ( ( kpair @ X16 @ X17 )
      = ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) @ emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).

thf(c_0_8,negated_conjecture,
    ! [X18: $i,X19: $i,X24: $i,X25: $i] :
      ( ( in @ ( esk1_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ ( esk2_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
      & ( ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ ( setadjoin @ ( esk2_2 @ X18 @ X19 ) @ emptyset ) ) @ emptyset ) ) )
      & ( ~ ( in @ X24 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
        | ~ ( in @ X25 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
        | ( ( kpair @ esk3_0 @ esk4_0 )
         != ( setadjoin @ ( setadjoin @ X24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X24 @ ( setadjoin @ X25 @ emptyset ) ) @ emptyset ) ) ) ) ),
    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_6])])])])]) ).

thf(c_0_9,plain,
    ! [X26: $i,X27: $i] :
      ( ( kpair @ X26 @ X27 )
      = ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X27 @ emptyset ) ) @ emptyset ) ) ),
    inference(variable_rename,[status(thm)],[c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
      | ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
      | ( ( kpair @ esk3_0 @ esk4_0 )
       != ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_11,plain,
    ! [X1: $i,X2: $i] :
      ( ( kpair @ X1 @ X2 )
      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( kpair @ X1 @ X2 )
       != ( kpair @ esk3_0 @ esk4_0 ) )
      | ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
      | ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
    inference(rw,[status(thm)],[c_0_12,c_0_11]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ ( setadjoin @ ( esk2_2 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: $i] :
      ( ( ( kpair @ X1 @ ( esk2_2 @ esk3_0 @ esk4_0 ) )
       != ( kpair @ esk3_0 @ esk4_0 ) )
      | ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( kpair @ ( esk1_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
      = ( kpair @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_11]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
    inference(rw,[status(thm)],[c_0_16,c_0_11]) ).

thf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n025.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 17:52:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.22/0.48  Running higher-order theorem proving
% 0.22/0.48  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
% 0.22/0.50  # Version: 3.1.0-ho
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50  # Starting sh4l with 300s (1) cores
% 0.22/0.50  # Starting ho_unfolding_2 with 300s (1) cores
% 0.22/0.50  # post_as_ho5 with pid 24007 completed with status 0
% 0.22/0.50  # Result found by post_as_ho5
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.50  # Search class: HUHSM-FFSF21-MSFFMFNN
% 0.22/0.50  # partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # new_ho_10 with pid 24012 completed with status 0
% 0.22/0.50  # Result found by new_ho_10
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.50  # Search class: HUHSM-FFSF21-MSFFMFNN
% 0.22/0.50  # partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # Preprocessing time       : 0.001 s
% 0.22/0.50  # Presaturation interreduction done
% 0.22/0.50  
% 0.22/0.50  # Proof found!
% 0.22/0.50  # SZS status Theorem
% 0.22/0.50  # SZS output start CNFRefutation
% See solution above
% 0.22/0.50  # Parsed axioms                        : 11
% 0.22/0.50  # Removed by relevancy pruning/SinE    : 7
% 0.22/0.50  # Initial clauses                      : 5
% 0.22/0.50  # Removed in clause preprocessing      : 0
% 0.22/0.50  # Initial clauses in saturation        : 5
% 0.22/0.50  # Processed clauses                    : 12
% 0.22/0.50  # ...of these trivial                  : 0
% 0.22/0.50  # ...subsumed                          : 0
% 0.22/0.50  # ...remaining for further processing  : 12
% 0.22/0.50  # Other redundant clauses eliminated   : 0
% 0.22/0.50  # Clauses deleted for lack of memory   : 0
% 0.22/0.50  # Backward-subsumed                    : 0
% 0.22/0.50  # Backward-rewritten                   : 0
% 0.22/0.50  # Generated clauses                    : 6
% 0.22/0.50  # ...of the previous two non-redundant : 5
% 0.22/0.50  # ...aggressively subsumed             : 0
% 0.22/0.50  # Contextual simplify-reflections      : 0
% 0.22/0.50  # Paramodulations                      : 6
% 0.22/0.50  # Factorizations                       : 0
% 0.22/0.50  # NegExts                              : 0
% 0.22/0.50  # Equation resolutions                 : 0
% 0.22/0.50  # Disequality decompositions           : 0
% 0.22/0.50  # Total rewrite steps                  : 6
% 0.22/0.50  # ...of those cached                   : 3
% 0.22/0.50  # Propositional unsat checks           : 0
% 0.22/0.50  #    Propositional check models        : 0
% 0.22/0.50  #    Propositional check unsatisfiable : 0
% 0.22/0.50  #    Propositional clauses             : 0
% 0.22/0.50  #    Propositional clauses after purity: 0
% 0.22/0.50  #    Propositional unsat core size     : 0
% 0.22/0.50  #    Propositional preprocessing time  : 0.000
% 0.22/0.50  #    Propositional encoding time       : 0.000
% 0.22/0.50  #    Propositional solver time         : 0.000
% 0.22/0.50  #    Success case prop preproc time    : 0.000
% 0.22/0.50  #    Success case prop encoding time   : 0.000
% 0.22/0.50  #    Success case prop solver time     : 0.000
% 0.22/0.50  # Current number of processed clauses  : 7
% 0.22/0.50  #    Positive orientable unit clauses  : 4
% 0.22/0.50  #    Positive unorientable unit clauses: 0
% 0.22/0.50  #    Negative unit clauses             : 0
% 0.22/0.50  #    Non-unit-clauses                  : 3
% 0.22/0.50  # Current number of unprocessed clauses: 3
% 0.22/0.50  # ...number of literals in the above   : 3
% 0.22/0.50  # Current number of archived formulas  : 0
% 0.22/0.50  # Current number of archived clauses   : 5
% 0.22/0.50  # Clause-clause subsumption calls (NU) : 6
% 0.22/0.50  # Rec. Clause-clause subsumption calls : 2
% 0.22/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.22/0.50  # Unit Clause-clause subsumption calls : 0
% 0.22/0.50  # Rewrite failures with RHS unbound    : 0
% 0.22/0.50  # BW rewrite match attempts            : 0
% 0.22/0.50  # BW rewrite match successes           : 0
% 0.22/0.50  # Condensation attempts                : 12
% 0.22/0.50  # Condensation successes               : 0
% 0.22/0.50  # Termbank termtop insertions          : 1047
% 0.22/0.50  # Search garbage collected termcells   : 179
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.004 s
% 0.22/0.50  # System time              : 0.002 s
% 0.22/0.50  # Total time               : 0.006 s
% 0.22/0.50  # Maximum resident set size: 1740 pages
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.005 s
% 0.22/0.50  # System time              : 0.005 s
% 0.22/0.50  # Total time               : 0.009 s
% 0.22/0.50  # Maximum resident set size: 1696 pages
% 0.22/0.50  % E---3.1 exiting
% 0.22/0.50  % E exiting
%------------------------------------------------------------------------------