TSTP Solution File: SEU805^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 03:30:25 EDT 2024

% Result   : Theorem 0.21s 0.50s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   33 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :   77 (  25 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  205 (  28   ~;  17   |;  14   &; 128   @)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   50 (   2   ^  35   !;  13   ?;  50   :)

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

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

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

thf(decl_25,type,
    nonempty: $i > $o ).

thf(decl_26,type,
    nonemptyE1: $o ).

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

thf(decl_28,type,
    disjointsetsI1: $o ).

thf(decl_29,type,
    esk1_1: $i > $i ).

thf(decl_30,type,
    esk2_1: $i > $i ).

thf(decl_31,type,
    esk3_2: $i > $i > $i ).

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

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

thf(nonemptyE1,axiom,
    ( nonemptyE1
  <=> ! [X1: $i] :
        ( ( nonempty @ X1 )
       => ? [X2: $i] : ( in @ X2 @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).

thf(foundation2,conjecture,
    ( foundationAx
   => ( nonemptyE1
     => ( disjointsetsI1
       => ! [X1: $i] :
            ( ( nonempty @ X1 )
           => ? [X4: $i] :
                ( ( in @ X4 @ X1 )
                & ( ( binintersect @ X4 @ X1 )
                  = emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2) ).

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

thf(disjointsetsI1,axiom,
    ( disjointsetsI1
  <=> ! [X1: $i,X3: $i] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X1 )
              & ( in @ X2 @ X3 ) )
       => ( ( binintersect @ X1 @ X3 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).

thf(c_0_5,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_6,axiom,
    ( nonemptyE1
    = ( ! [X1: $i] :
          ( ( X1 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_5]) ).

thf(c_0_7,negated_conjecture,
    ~ ( ! [X16: $i] :
          ( ? [X17: $i] : ( in @ X17 @ X16 )
         => ? [X18: $i] :
              ( ( in @ X18 @ X16 )
              & ~ ? [X19: $i] :
                    ( ( in @ X19 @ X18 )
                    & ( in @ X19 @ X16 ) ) ) )
     => ( ! [X20: $i] :
            ( ( X20 != emptyset )
           => ? [X21: $i] : ( in @ X21 @ X20 ) )
       => ( ! [X22: $i,X23: $i] :
              ( ~ ? [X24: $i] :
                    ( ( in @ X24 @ X22 )
                    & ( in @ X24 @ X23 ) )
             => ( ( binintersect @ X22 @ X23 )
                = emptyset ) )
         => ! [X1: $i] :
              ( ( X1 != emptyset )
             => ? [X4: $i] :
                  ( ( in @ X4 @ X1 )
                  & ( ( binintersect @ X4 @ X1 )
                    = emptyset ) ) ) ) ) ),
    inference(fof_simplification,[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)],[foundation2]),c_0_5]),c_0_6]),foundationAx]),disjointsetsI1])]) ).

thf(c_0_8,negated_conjecture,
    ! [X25: $i,X26: $i,X28: $i,X29: $i,X31: $i,X32: $i,X35: $i] :
      ( ( ( in @ ( esk1_1 @ X25 ) @ X25 )
        | ~ ( in @ X26 @ X25 ) )
      & ( ~ ( in @ X28 @ ( esk1_1 @ X25 ) )
        | ~ ( in @ X28 @ X25 )
        | ~ ( in @ X26 @ X25 ) )
      & ( ( X29 = emptyset )
        | ( in @ ( esk2_1 @ X29 ) @ X29 ) )
      & ( ( in @ ( esk3_2 @ X31 @ X32 ) @ X31 )
        | ( ( binintersect @ X31 @ X32 )
          = emptyset ) )
      & ( ( in @ ( esk3_2 @ X31 @ X32 ) @ X32 )
        | ( ( binintersect @ X31 @ X32 )
          = emptyset ) )
      & ( esk4_0 != emptyset )
      & ( ~ ( in @ X35 @ esk4_0 )
        | ( ( binintersect @ X35 @ esk4_0 )
         != emptyset ) ) ),
    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_7])])])])])]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ~ ( in @ X1 @ ( esk1_1 @ X2 ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X3 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( in @ X1 @ ( esk1_1 @ X2 ) )
      | ~ ( in @ X1 @ X2 ) ),
    inference(condense,[status(thm)],[c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( esk3_2 @ X1 @ X2 ) @ X1 )
      | ( ( binintersect @ X1 @ X2 )
        = emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( binintersect @ ( esk1_1 @ X1 ) @ X2 )
        = emptyset )
      | ~ ( in @ ( esk3_2 @ ( esk1_1 @ X1 ) @ X2 ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( esk3_2 @ X1 @ X2 ) @ X2 )
      | ( ( binintersect @ X1 @ X2 )
        = emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( in @ X1 @ esk4_0 )
      | ( ( binintersect @ X1 @ esk4_0 )
       != emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] :
      ( ( binintersect @ ( esk1_1 @ X1 ) @ X1 )
      = emptyset ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( in @ ( esk1_1 @ X1 ) @ X1 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: $i] :
      ( ( X1 = emptyset )
      | ( in @ ( esk2_1 @ X1 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_18,negated_conjecture,
    ~ ( in @ ( esk1_1 @ esk4_0 ) @ esk4_0 ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i] :
      ( ( X1 = emptyset )
      | ( in @ ( esk1_1 @ X1 ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_20,negated_conjecture,
    esk4_0 != emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 18:16:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.48  Running higher-order theorem proving
% 0.21/0.48  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
% 0.21/0.50  # Version: 3.1.0-ho
% 0.21/0.50  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.50  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.50  # Starting lpo1_def_fix with 300s (1) cores
% 0.21/0.50  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.21/0.50  # ehoh_best_sine_rwall with pid 10627 completed with status 0
% 0.21/0.50  # Result found by ehoh_best_sine_rwall
% 0.21/0.50  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.50  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.50  # Search class: HGHSF-FFSF21-SSFFMFNN
% 0.21/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50  # new_ho_10 with pid 10630 completed with status 0
% 0.21/0.50  # Result found by new_ho_10
% 0.21/0.50  # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.50  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.50  # Search class: HGHSF-FFSF21-SSFFMFNN
% 0.21/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50  # Preprocessing time       : 0.001 s
% 0.21/0.50  # Presaturation interreduction done
% 0.21/0.50  
% 0.21/0.50  # Proof found!
% 0.21/0.50  # SZS status Theorem
% 0.21/0.50  # SZS output start CNFRefutation
% See solution above
% 0.21/0.50  # Parsed axioms                        : 12
% 0.21/0.50  # Removed by relevancy pruning/SinE    : 7
% 0.21/0.50  # Initial clauses                      : 7
% 0.21/0.50  # Removed in clause preprocessing      : 0
% 0.21/0.50  # Initial clauses in saturation        : 7
% 0.21/0.50  # Processed clauses                    : 25
% 0.21/0.50  # ...of these trivial                  : 0
% 0.21/0.50  # ...subsumed                          : 1
% 0.21/0.50  # ...remaining for further processing  : 24
% 0.21/0.50  # Other redundant clauses eliminated   : 0
% 0.21/0.50  # Clauses deleted for lack of memory   : 0
% 0.21/0.50  # Backward-subsumed                    : 0
% 0.21/0.50  # Backward-rewritten                   : 0
% 0.21/0.50  # Generated clauses                    : 19
% 0.21/0.50  # ...of the previous two non-redundant : 17
% 0.21/0.50  # ...aggressively subsumed             : 0
% 0.21/0.50  # Contextual simplify-reflections      : 0
% 0.21/0.50  # Paramodulations                      : 19
% 0.21/0.50  # Factorizations                       : 0
% 0.21/0.50  # NegExts                              : 0
% 0.21/0.50  # Equation resolutions                 : 0
% 0.21/0.50  # Disequality decompositions           : 0
% 0.21/0.50  # Total rewrite steps                  : 0
% 0.21/0.50  # ...of those cached                   : 0
% 0.21/0.50  # Propositional unsat checks           : 0
% 0.21/0.50  #    Propositional check models        : 0
% 0.21/0.50  #    Propositional check unsatisfiable : 0
% 0.21/0.50  #    Propositional clauses             : 0
% 0.21/0.50  #    Propositional clauses after purity: 0
% 0.21/0.50  #    Propositional unsat core size     : 0
% 0.21/0.50  #    Propositional preprocessing time  : 0.000
% 0.21/0.50  #    Propositional encoding time       : 0.000
% 0.21/0.50  #    Propositional solver time         : 0.000
% 0.21/0.50  #    Success case prop preproc time    : 0.000
% 0.21/0.50  #    Success case prop encoding time   : 0.000
% 0.21/0.50  #    Success case prop solver time     : 0.000
% 0.21/0.50  # Current number of processed clauses  : 17
% 0.21/0.50  #    Positive orientable unit clauses  : 2
% 0.21/0.50  #    Positive unorientable unit clauses: 0
% 0.21/0.50  #    Negative unit clauses             : 2
% 0.21/0.50  #    Non-unit-clauses                  : 13
% 0.21/0.50  # Current number of unprocessed clauses: 5
% 0.21/0.50  # ...number of literals in the above   : 10
% 0.21/0.50  # Current number of archived formulas  : 0
% 0.21/0.50  # Current number of archived clauses   : 7
% 0.21/0.50  # Clause-clause subsumption calls (NU) : 25
% 0.21/0.50  # Rec. Clause-clause subsumption calls : 25
% 0.21/0.50  # Non-unit clause-clause subsumptions  : 2
% 0.21/0.50  # Unit Clause-clause subsumption calls : 8
% 0.21/0.50  # Rewrite failures with RHS unbound    : 0
% 0.21/0.50  # BW rewrite match attempts            : 2
% 0.21/0.50  # BW rewrite match successes           : 0
% 0.21/0.50  # Condensation attempts                : 25
% 0.21/0.50  # Condensation successes               : 1
% 0.21/0.50  # Termbank termtop insertions          : 1129
% 0.21/0.50  # Search garbage collected termcells   : 320
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.003 s
% 0.21/0.50  # System time              : 0.003 s
% 0.21/0.50  # Total time               : 0.006 s
% 0.21/0.50  # Maximum resident set size: 1740 pages
% 0.21/0.50  
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.003 s
% 0.21/0.50  # System time              : 0.006 s
% 0.21/0.50  # Total time               : 0.009 s
% 0.21/0.50  # Maximum resident set size: 1708 pages
% 0.21/0.50  % E---3.1 exiting
% 0.21/0.50  % E exiting
%------------------------------------------------------------------------------