TSTP Solution File: SEU517^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU517^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 03:27:54 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   36 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :  102 (  21 equ;   0 cnn)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  355 (  27   ~;  38   |;   7   &; 254   @)
%                                         (   6 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   78 (   7   ^  71   !;   0   ?;  78   :)

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

thf(decl_23,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(decl_24,type,
    dsetconstrI: $o ).

thf(decl_25,type,
    dsetconstrEL: $o ).

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

thf(decl_27,type,
    esk1_2: $i > $i > $i ).

thf(decl_28,type,
    esk2_2: $i > $i > $i ).

thf(decl_29,type,
    esk3_0: $i ).

thf(decl_30,type,
    epred1_0: $i > $o ).

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

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

thf(setoftrueEq,conjecture,
    ( dsetconstrI
   => ( dsetconstrEL
     => ( setext
       => ! [X1: $i] :
            ( ( dsetconstr @ X1
              @ ^ [X3: $i] : $true )
            = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).

thf(setext,axiom,
    ( setext
  <=> ! [X1: $i,X5: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X5 ) )
       => ( ! [X3: $i] :
              ( ( in @ X3 @ X5 )
             => ( in @ X3 @ X1 ) )
         => ( X1 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).

thf(c_0_4,plain,
    ( dsetconstrI
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ( ( X2 @ X3 )
         => ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrI]) ).

thf(c_0_5,plain,
    ( dsetconstrEL
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
       => ( in @ X3 @ X1 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).

thf(c_0_6,negated_conjecture,
    ~ ( ! [X17: $i,X18: $i > $o,X19: $i] :
          ( ( in @ X19 @ X17 )
         => ( ( X18 @ X19 )
           => ( in @ X19 @ ( dsetconstr @ X17 @ X18 ) ) ) )
     => ( ! [X20: $i,X21: $i > $o,X22: $i] :
            ( ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
           => ( in @ X22 @ X20 ) )
       => ( ! [X23: $i,X24: $i] :
              ( ! [X25: $i] :
                  ( ( in @ X25 @ X23 )
                 => ( in @ X25 @ X24 ) )
             => ( ! [X26: $i] :
                    ( ( in @ X26 @ X24 )
                   => ( in @ X26 @ X23 ) )
               => ( X23 = X24 ) ) )
         => ! [X1: $i] :
              ( ( dsetconstr @ X1
                @ ^ [Z0: $i] : $true )
              = X1 ) ) ) ),
    inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[setoftrueEq])]),c_0_4]),c_0_5]),setext])]) ).

thf(c_0_7,negated_conjecture,
    ! [X27: $i,X28: $i > $o,X29: $i,X30: $i,X31: $i > $o,X32: $i,X33: $i,X34: $i] :
      ( ( ~ ( in @ X29 @ X27 )
        | ~ ( X28 @ X29 )
        | ( in @ X29 @ ( dsetconstr @ X27 @ X28 ) ) )
      & ( ~ ( in @ X32 @ ( dsetconstr @ X30 @ X31 ) )
        | ( in @ X32 @ X30 ) )
      & ( ( in @ ( esk2_2 @ X33 @ X34 ) @ X34 )
        | ( X33 = X34 )
        | ( in @ ( esk1_2 @ X33 @ X34 ) @ X33 ) )
      & ( ~ ( in @ ( esk2_2 @ X33 @ X34 ) @ X33 )
        | ( X33 = X34 )
        | ( in @ ( esk1_2 @ X33 @ X34 ) @ X33 ) )
      & ( ( in @ ( esk2_2 @ X33 @ X34 ) @ X34 )
        | ( X33 = X34 )
        | ~ ( in @ ( esk1_2 @ X33 @ X34 ) @ X34 ) )
      & ( ~ ( in @ ( esk2_2 @ X33 @ X34 ) @ X33 )
        | ( X33 = X34 )
        | ~ ( in @ ( esk1_2 @ X33 @ X34 ) @ X34 ) )
      & ( ( dsetconstr @ esk3_0
          @ ^ [Z0: $i] : $true )
       != 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_6])])])])])]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( in @ X1 @ X3 )
      | ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( in @ ( esk2_2 @ X1 @ X3 ) @ X3 )
      | ( X1 = X3 )
      | ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,plain,
    ! [X39: $i] :
      ( ( ~ ( epred1_0 @ X39 )
        | $true )
      & ( ~ $true
        | ( epred1_0 @ X39 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( X1
        = ( dsetconstr @ X3 @ X2 ) )
      | ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 )
      | ~ ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ ( dsetconstr @ X3 @ X2 ) ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
      | ~ ( in @ X1 @ X3 )
      | ~ ( X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_13,plain,
    ! [X1: $i] :
      ( ( epred1_0 @ X1 )
      | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_14,negated_conjecture,
    ! [X3: $i,X1: $i] :
      ( ( in @ ( esk2_2 @ X1 @ X3 ) @ X3 )
      | ( X1 = X3 )
      | ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( X1 = X3 )
      | ~ ( in @ ( esk2_2 @ X1 @ X3 ) @ X1 )
      | ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( X1
        = ( dsetconstr @ X3 @ X2 ) )
      | ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 )
      | ~ ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 )
      | ~ ( X2 @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_17,plain,
    ! [X1: $i] : ( epred1_0 @ X1 ),
    inference(cn,[status(thm)],[c_0_13]) ).

thf(c_0_18,negated_conjecture,
    ! [X3: $i,X1: $i] :
      ( ( X1 = X3 )
      | ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_2 @ X1 @ X3 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( X1
        = ( dsetconstr @ X3 @ X2 ) )
      | ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X1 )
      | ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_14]) ).

thf(c_0_20,plain,
    ! [X38: $i] :
      ( ( epred1_0 @ X38 )
    <=> $true ),
    introduced(definition) ).

thf(c_0_21,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( X1
        = ( dsetconstr @ X3 @ X2 ) )
      | ~ ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X1 )
      | ~ ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 )
      | ~ ( X2 @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_12]) ).

thf(c_0_22,plain,
    ! [X1: $i,X3: $i] :
      ( ( X1
        = ( dsetconstr @ X3 @ epred1_0 ) )
      | ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ epred1_0 ) ) @ X3 )
      | ~ ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ epred1_0 ) ) @ X3 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( ( dsetconstr @ X1 @ X2 )
        = X1 )
      | ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_24,negated_conjecture,
    ( ( dsetconstr @ esk3_0 @ epred1_0 )
   != esk3_0 ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]),c_0_20]) ).

thf(c_0_25,negated_conjecture,
    ! [X1: $i] :
      ( ( dsetconstr @ X1 @ epred1_0 )
      = X1 ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17])]),c_0_23]) ).

thf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU517^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n002.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 16:15:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 0.19/0.49  # Version: 3.1.0-ho
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSSA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_2 with 300s (1) cores
% 0.19/0.49  # Starting new_bool_9 with 300s (1) cores
% 0.19/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.49  # new_ho_10 with pid 9175 completed with status 0
% 0.19/0.49  # Result found by new_ho_10
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSSA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49  # No SInE strategy applied
% 0.19/0.49  # Search class: HGUSF-FFSF22-SSSFMSBN
% 0.19/0.49  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49  # Starting new_ho_10 with 901s (1) cores
% 0.19/0.49  # Starting new_bool_2 with 151s (1) cores
% 0.19/0.49  # Starting new_bool_9 with 151s (1) cores
% 0.19/0.49  # Starting ehoh_best8_lambda with 151s (1) cores
% 0.19/0.49  # Starting new_bool_3 with 146s (1) cores
% 0.19/0.49  # new_ho_10 with pid 9182 completed with status 0
% 0.19/0.49  # Result found by new_ho_10
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSSA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49  # No SInE strategy applied
% 0.19/0.49  # Search class: HGUSF-FFSF22-SSSFMSBN
% 0.19/0.49  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49  # Starting new_ho_10 with 901s (1) cores
% 0.19/0.49  # Preprocessing time       : 0.001 s
% 0.19/0.49  # Presaturation interreduction done
% 0.19/0.49  
% 0.19/0.49  # Proof found!
% 0.19/0.49  # SZS status Theorem
% 0.19/0.49  # SZS output start CNFRefutation
% See solution above
% 0.19/0.49  # Parsed axioms                        : 9
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.49  # Initial clauses                      : 14
% 0.19/0.49  # Removed in clause preprocessing      : 6
% 0.19/0.49  # Initial clauses in saturation        : 8
% 0.19/0.49  # Processed clauses                    : 26
% 0.19/0.49  # ...of these trivial                  : 0
% 0.19/0.49  # ...subsumed                          : 0
% 0.19/0.49  # ...remaining for further processing  : 26
% 0.19/0.49  # Other redundant clauses eliminated   : 0
% 0.19/0.49  # Clauses deleted for lack of memory   : 0
% 0.19/0.49  # Backward-subsumed                    : 0
% 0.19/0.49  # Backward-rewritten                   : 2
% 0.19/0.49  # Generated clauses                    : 33
% 0.19/0.49  # ...of the previous two non-redundant : 20
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 1
% 0.19/0.49  # Paramodulations                      : 33
% 0.19/0.49  # Factorizations                       : 0
% 0.19/0.49  # NegExts                              : 0
% 0.19/0.49  # Equation resolutions                 : 0
% 0.19/0.49  # Disequality decompositions           : 0
% 0.19/0.49  # Total rewrite steps                  : 5
% 0.19/0.49  # ...of those cached                   : 2
% 0.19/0.49  # Propositional unsat checks           : 0
% 0.19/0.49  #    Propositional check models        : 0
% 0.19/0.49  #    Propositional check unsatisfiable : 0
% 0.19/0.49  #    Propositional clauses             : 0
% 0.19/0.49  #    Propositional clauses after purity: 0
% 0.19/0.49  #    Propositional unsat core size     : 0
% 0.19/0.49  #    Propositional preprocessing time  : 0.000
% 0.19/0.49  #    Propositional encoding time       : 0.000
% 0.19/0.49  #    Propositional solver time         : 0.000
% 0.19/0.49  #    Success case prop preproc time    : 0.000
% 0.19/0.49  #    Success case prop encoding time   : 0.000
% 0.19/0.49  #    Success case prop solver time     : 0.000
% 0.19/0.49  # Current number of processed clauses  : 16
% 0.19/0.49  #    Positive orientable unit clauses  : 2
% 0.19/0.49  #    Positive unorientable unit clauses: 0
% 0.19/0.49  #    Negative unit clauses             : 0
% 0.19/0.49  #    Non-unit-clauses                  : 14
% 0.19/0.49  # Current number of unprocessed clauses: 9
% 0.19/0.49  # ...number of literals in the above   : 30
% 0.19/0.49  # Current number of archived formulas  : 0
% 0.19/0.49  # Current number of archived clauses   : 10
% 0.19/0.49  # Clause-clause subsumption calls (NU) : 89
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 49
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 1
% 0.19/0.49  # Unit Clause-clause subsumption calls : 0
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 3
% 0.19/0.49  # BW rewrite match successes           : 2
% 0.19/0.49  # Condensation attempts                : 26
% 0.19/0.49  # Condensation successes               : 0
% 0.19/0.49  # Termbank termtop insertions          : 1930
% 0.19/0.49  # Search garbage collected termcells   : 394
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.008 s
% 0.19/0.49  # System time              : 0.001 s
% 0.19/0.49  # Total time               : 0.009 s
% 0.19/0.49  # Maximum resident set size: 1848 pages
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.022 s
% 0.19/0.49  # System time              : 0.006 s
% 0.19/0.49  # Total time               : 0.028 s
% 0.19/0.49  # Maximum resident set size: 1708 pages
% 0.19/0.49  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------