TSTP Solution File: SEU651^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU651^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 03:28:51 EDT 2024

% Result   : Theorem 0.20s 0.51s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   30 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :   46 (  29 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  278 (   8   ~;   4   |;   5   &; 244   @)
%                                         (   3 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  33   !;   0   ?;  33   :)

% 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,
    uniqinunit: $o ).

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

thf(decl_27,type,
    setukpairinjR12: $o ).

thf(decl_28,type,
    esk1_0: $i ).

thf(decl_29,type,
    esk2_0: $i ).

thf(decl_30,type,
    esk3_0: $i ).

thf(decl_31,type,
    esk4_0: $i ).

thf(setukpairinjR1,conjecture,
    ( uniqinunit
   => ( secondinupair
     => ( setukpairinjR12
       => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( ( X3 = X4 )
             => ( X2 = X4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(secondinupair,axiom,
    ( secondinupair
  <=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).

thf(setukpairinjR12,axiom,
    ( setukpairinjR12
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).

thf(c_0_4,negated_conjecture,
    ~ ( ! [X15: $i,X16: $i] :
          ( ( in @ X15 @ ( setadjoin @ X16 @ emptyset ) )
         => ( X15 = X16 ) )
     => ( ! [X17: $i,X18: $i] : ( in @ X18 @ ( setadjoin @ X17 @ ( setadjoin @ X18 @ emptyset ) ) )
       => ( ! [X19: $i,X20: $i] :
              ( ( X19 = X20 )
             => ( ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X19 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ emptyset ) ) )
         => ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
             => ( ( X3 = X4 )
               => ( X2 = X4 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setukpairinjR1]),uniqinunit]),secondinupair]),setukpairinjR12]) ).

thf(c_0_5,negated_conjecture,
    ! [X21: $i,X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
      ( ( ~ ( in @ X21 @ ( setadjoin @ X22 @ emptyset ) )
        | ( X21 = X22 ) )
      & ( in @ X24 @ ( setadjoin @ X23 @ ( setadjoin @ X24 @ emptyset ) ) )
      & ( ( X25 != X26 )
        | ( ( setadjoin @ ( setadjoin @ X25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X25 @ ( setadjoin @ X26 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X25 @ emptyset ) @ emptyset ) ) )
      & ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) )
      & ( esk3_0 = esk4_0 )
      & ( esk2_0 != esk4_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_4])])])])]) ).

thf(c_0_6,negated_conjecture,
    ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
    = ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_7,negated_conjecture,
    esk3_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) )
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,negated_conjecture,
    ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
    = ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ emptyset ) ) ),
    inference(rw,[status(thm)],[c_0_6,c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i] :
      ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ),
    inference(er,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_12,negated_conjecture,
    ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
    = ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_14,negated_conjecture,
    in @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_15,negated_conjecture,
    ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
    = ( setadjoin @ esk3_0 @ emptyset ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_16,negated_conjecture,
    esk2_0 != esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_17,negated_conjecture,
    in @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

thf(c_0_18,negated_conjecture,
    esk2_0 != esk3_0,
    inference(rw,[status(thm)],[c_0_16,c_0_7]) ).

thf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU651^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 17:26:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.50  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
% 0.20/0.51  # Version: 3.1.0-ho
% 0.20/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho2 with 300s (1) cores
% 0.20/0.51  # post_as_ho3 with pid 8758 completed with status 0
% 0.20/0.51  # Result found by post_as_ho3
% 0.20/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.51  # No SInE strategy applied
% 0.20/0.51  # Search class: HHUSF-FFSF22-MFFFMFNN
% 0.20/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51  # new_ho_10 with pid 8762 completed with status 0
% 0.20/0.51  # Result found by new_ho_10
% 0.20/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.51  # No SInE strategy applied
% 0.20/0.51  # Search class: HHUSF-FFSF22-MFFFMFNN
% 0.20/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51  # Preprocessing time       : 0.001 s
% 0.20/0.51  # Presaturation interreduction done
% 0.20/0.51  
% 0.20/0.51  # Proof found!
% 0.20/0.51  # SZS status Theorem
% 0.20/0.51  # SZS output start CNFRefutation
% See solution above
% 0.20/0.51  # Parsed axioms                        : 10
% 0.20/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.51  # Initial clauses                      : 12
% 0.20/0.51  # Removed in clause preprocessing      : 6
% 0.20/0.51  # Initial clauses in saturation        : 6
% 0.20/0.51  # Processed clauses                    : 19
% 0.20/0.51  # ...of these trivial                  : 0
% 0.20/0.51  # ...subsumed                          : 0
% 0.20/0.51  # ...remaining for further processing  : 19
% 0.20/0.51  # Other redundant clauses eliminated   : 1
% 0.20/0.51  # Clauses deleted for lack of memory   : 0
% 0.20/0.51  # Backward-subsumed                    : 0
% 0.20/0.51  # Backward-rewritten                   : 2
% 0.20/0.51  # Generated clauses                    : 8
% 0.20/0.51  # ...of the previous two non-redundant : 9
% 0.20/0.51  # ...aggressively subsumed             : 0
% 0.20/0.51  # Contextual simplify-reflections      : 0
% 0.20/0.51  # Paramodulations                      : 7
% 0.20/0.51  # Factorizations                       : 0
% 0.20/0.51  # NegExts                              : 0
% 0.20/0.51  # Equation resolutions                 : 1
% 0.20/0.51  # Disequality decompositions           : 0
% 0.20/0.51  # Total rewrite steps                  : 4
% 0.20/0.51  # ...of those cached                   : 1
% 0.20/0.51  # Propositional unsat checks           : 0
% 0.20/0.51  #    Propositional check models        : 0
% 0.20/0.51  #    Propositional check unsatisfiable : 0
% 0.20/0.51  #    Propositional clauses             : 0
% 0.20/0.51  #    Propositional clauses after purity: 0
% 0.20/0.51  #    Propositional unsat core size     : 0
% 0.20/0.51  #    Propositional preprocessing time  : 0.000
% 0.20/0.51  #    Propositional encoding time       : 0.000
% 0.20/0.51  #    Propositional solver time         : 0.000
% 0.20/0.51  #    Success case prop preproc time    : 0.000
% 0.20/0.51  #    Success case prop encoding time   : 0.000
% 0.20/0.51  #    Success case prop solver time     : 0.000
% 0.20/0.51  # Current number of processed clauses  : 10
% 0.20/0.51  #    Positive orientable unit clauses  : 8
% 0.20/0.52  #    Positive unorientable unit clauses: 0
% 0.20/0.52  #    Negative unit clauses             : 1
% 0.20/0.52  #    Non-unit-clauses                  : 1
% 0.20/0.52  # Current number of unprocessed clauses: 2
% 0.20/0.52  # ...number of literals in the above   : 2
% 0.20/0.52  # Current number of archived formulas  : 0
% 0.20/0.52  # Current number of archived clauses   : 8
% 0.20/0.52  # Clause-clause subsumption calls (NU) : 0
% 0.20/0.52  # Rec. Clause-clause subsumption calls : 0
% 0.20/0.52  # Non-unit clause-clause subsumptions  : 0
% 0.20/0.52  # Unit Clause-clause subsumption calls : 0
% 0.20/0.52  # Rewrite failures with RHS unbound    : 0
% 0.20/0.52  # BW rewrite match attempts            : 4
% 0.20/0.52  # BW rewrite match successes           : 2
% 0.20/0.52  # Condensation attempts                : 19
% 0.20/0.52  # Condensation successes               : 0
% 0.20/0.52  # Termbank termtop insertions          : 925
% 0.20/0.52  # Search garbage collected termcells   : 224
% 0.20/0.52  
% 0.20/0.52  # -------------------------------------------------
% 0.20/0.52  # User time                : 0.006 s
% 0.20/0.52  # System time              : 0.000 s
% 0.20/0.52  # Total time               : 0.006 s
% 0.20/0.52  # Maximum resident set size: 1740 pages
% 0.20/0.52  
% 0.20/0.52  # -------------------------------------------------
% 0.20/0.52  # User time                : 0.007 s
% 0.20/0.52  # System time              : 0.003 s
% 0.20/0.52  # Total time               : 0.011 s
% 0.20/0.52  # Maximum resident set size: 1704 pages
% 0.20/0.52  % E---3.1 exiting
% 0.20/0.52  % E exiting
%------------------------------------------------------------------------------