TSTP Solution File: SEU742^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU742^2 : 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 03:29:45 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   34 (   8 unt;  12 typ;   0 def)
%            Number of atoms       :  108 (   0 equ;   0 cnn)
%            Maximal formula atoms :   21 (   4 avg)
%            Number of connectives :  458 (  40   ~;  35   |;   8   &; 332   @)
%                                         (   3 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   68 (   0   ^  68   !;   0   ?;  68   :)

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

thf(decl_23,type,
    powerset: $i > $i ).

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

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

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

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

thf(decl_28,type,
    inIntersectImpInUnion2: $o ).

thf(decl_29,type,
    esk1_0: $i ).

thf(decl_30,type,
    esk2_0: $i ).

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

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

thf(decl_33,type,
    esk5_0: $i ).

thf(inIntersectImpInIntersectUnions,conjecture,
    ( binintersectI
   => ( inIntersectImpInUnion
     => ( inIntersectImpInUnion2
       => ! [X1: $i,X4: $i] :
            ( ( in @ X4 @ ( powerset @ X1 ) )
           => ! [X5: $i] :
                ( ( in @ X5 @ ( powerset @ X1 ) )
               => ! [X6: $i] :
                    ( ( in @ X6 @ ( powerset @ X1 ) )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
                         => ( in @ X3 @ ( binintersect @ ( binunion @ X4 @ X6 ) @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).

thf(inIntersectImpInUnion2,axiom,
    ( inIntersectImpInUnion2
  <=> ! [X1: $i,X4: $i] :
        ( ( in @ X4 @ ( powerset @ X1 ) )
       => ! [X5: $i] :
            ( ( in @ X5 @ ( powerset @ X1 ) )
           => ! [X6: $i] :
                ( ( in @ X6 @ ( powerset @ X1 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
                     => ( in @ X3 @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).

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

thf(inIntersectImpInUnion,axiom,
    ( inIntersectImpInUnion
  <=> ! [X1: $i,X4: $i] :
        ( ( in @ X4 @ ( powerset @ X1 ) )
       => ! [X5: $i] :
            ( ( in @ X5 @ ( powerset @ X1 ) )
           => ! [X6: $i] :
                ( ( in @ X6 @ ( powerset @ X1 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
                     => ( in @ X3 @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).

thf(c_0_4,negated_conjecture,
    ~ ( ! [X25: $i,X26: $i,X27: $i] :
          ( ( in @ X27 @ X25 )
         => ( ( in @ X27 @ X26 )
           => ( in @ X27 @ ( binintersect @ X25 @ X26 ) ) ) )
     => ( ! [X28: $i,X29: $i] :
            ( ( in @ X29 @ ( powerset @ X28 ) )
           => ! [X30: $i] :
                ( ( in @ X30 @ ( powerset @ X28 ) )
               => ! [X31: $i] :
                    ( ( in @ X31 @ ( powerset @ X28 ) )
                   => ! [X32: $i] :
                        ( ( in @ X32 @ X28 )
                       => ( ( in @ X32 @ ( binintersect @ X29 @ X30 ) )
                         => ( in @ X32 @ ( binunion @ X29 @ X31 ) ) ) ) ) ) )
       => ( ! [X33: $i,X34: $i] :
              ( ( in @ X34 @ ( powerset @ X33 ) )
             => ! [X35: $i] :
                  ( ( in @ X35 @ ( powerset @ X33 ) )
                 => ! [X36: $i] :
                      ( ( in @ X36 @ ( powerset @ X33 ) )
                     => ! [X37: $i] :
                          ( ( in @ X37 @ X33 )
                         => ( ( in @ X37 @ ( binintersect @ X34 @ X35 ) )
                           => ( in @ X37 @ ( binunion @ X35 @ X36 ) ) ) ) ) ) )
         => ! [X1: $i,X4: $i] :
              ( ( in @ X4 @ ( powerset @ X1 ) )
             => ! [X5: $i] :
                  ( ( in @ X5 @ ( powerset @ X1 ) )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ ( powerset @ X1 ) )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
                           => ( in @ X3 @ ( binintersect @ ( binunion @ X4 @ X6 ) @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[inIntersectImpInIntersectUnions]),inIntersectImpInUnion2]),binintersectI]),inIntersectImpInUnion]) ).

thf(c_0_5,negated_conjecture,
    ! [X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i] :
      ( ( ~ ( in @ X40 @ X38 )
        | ~ ( in @ X40 @ X39 )
        | ( in @ X40 @ ( binintersect @ X38 @ X39 ) ) )
      & ( ~ ( in @ X42 @ ( powerset @ X41 ) )
        | ~ ( in @ X43 @ ( powerset @ X41 ) )
        | ~ ( in @ X44 @ ( powerset @ X41 ) )
        | ~ ( in @ X45 @ X41 )
        | ~ ( in @ X45 @ ( binintersect @ X42 @ X43 ) )
        | ( in @ X45 @ ( binunion @ X42 @ X44 ) ) )
      & ( ~ ( in @ X47 @ ( powerset @ X46 ) )
        | ~ ( in @ X48 @ ( powerset @ X46 ) )
        | ~ ( in @ X49 @ ( powerset @ X46 ) )
        | ~ ( in @ X50 @ X46 )
        | ~ ( in @ X50 @ ( binintersect @ X47 @ X48 ) )
        | ( in @ X50 @ ( binunion @ X48 @ X49 ) ) )
      & ( in @ esk2_0 @ ( powerset @ esk1_0 ) )
      & ( in @ esk3_0 @ ( powerset @ esk1_0 ) )
      & ( in @ esk4_0 @ ( powerset @ esk1_0 ) )
      & ( in @ esk5_0 @ esk1_0 )
      & ( in @ esk5_0 @ ( binintersect @ esk2_0 @ esk3_0 ) )
      & ~ ( in @ esk5_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk4_0 ) @ ( binunion @ esk3_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,
    ! [X2: $i,X1: $i,X4: $i,X5: $i,X3: $i] :
      ( ( in @ X5 @ ( binunion @ X3 @ X4 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ X3 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X5 @ X2 )
      | ~ ( in @ X5 @ ( binintersect @ X1 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_7,negated_conjecture,
    in @ esk5_0 @ ( binintersect @ esk2_0 @ esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ~ ( in @ esk5_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk4_0 ) @ ( binunion @ esk3_0 @ esk4_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X1 @ ( binintersect @ X2 @ X3 ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ esk5_0 @ ( binunion @ esk3_0 @ X1 ) )
      | ~ ( in @ esk3_0 @ ( powerset @ X2 ) )
      | ~ ( in @ esk2_0 @ ( powerset @ X2 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ esk5_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

thf(c_0_11,negated_conjecture,
    in @ esk3_0 @ ( powerset @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_12,negated_conjecture,
    in @ esk2_0 @ ( powerset @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_13,negated_conjecture,
    in @ esk5_0 @ esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_14,negated_conjecture,
    ! [X2: $i,X1: $i,X4: $i,X5: $i,X3: $i] :
      ( ( in @ X5 @ ( binunion @ X1 @ X4 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ X3 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X5 @ X2 )
      | ~ ( in @ X5 @ ( binintersect @ X1 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_15,negated_conjecture,
    ( ~ ( in @ esk5_0 @ ( binunion @ esk3_0 @ esk4_0 ) )
    | ~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk4_0 ) ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i] :
      ( ( in @ esk5_0 @ ( binunion @ esk3_0 @ X1 ) )
      | ~ ( in @ X1 @ ( powerset @ esk1_0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).

thf(c_0_17,negated_conjecture,
    in @ esk4_0 @ ( powerset @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ esk5_0 @ ( binunion @ esk2_0 @ X1 ) )
      | ~ ( in @ esk3_0 @ ( powerset @ X2 ) )
      | ~ ( in @ esk2_0 @ ( powerset @ X2 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ esk5_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_7]) ).

thf(c_0_19,negated_conjecture,
    ~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk4_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: $i] :
      ( ( in @ esk5_0 @ ( binunion @ esk2_0 @ X1 ) )
      | ~ ( in @ X1 @ ( powerset @ esk1_0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_12]),c_0_13])]) ).

thf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun May 19 18:05:38 EDT 2024
% 0.12/0.34  % 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: HSSSSLSSSLSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.49  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.49  # Starting post_as_ho3 with 300s (1) cores
% 0.19/0.49  # Starting post_as_ho2 with 300s (1) cores
% 0.19/0.49  # post_as_ho8 with pid 25163 completed with status 0
% 0.19/0.49  # Result found by post_as_ho8
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.49  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.49  # Search class: HHUNF-FFSS21-SFFFMFNN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.49  # new_ho_10 with pid 25166 completed with status 0
% 0.19/0.49  # Result found by new_ho_10
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.49  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.49  # Search class: HHUNF-FFSS21-SFFFMFNN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting new_ho_10 with 163s (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                        : 11
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 7
% 0.19/0.49  # Initial clauses                      : 9
% 0.19/0.49  # Removed in clause preprocessing      : 0
% 0.19/0.49  # Initial clauses in saturation        : 9
% 0.19/0.49  # Processed clauses                    : 29
% 0.19/0.49  # ...of these trivial                  : 0
% 0.19/0.49  # ...subsumed                          : 1
% 0.19/0.49  # ...remaining for further processing  : 28
% 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                    : 1
% 0.19/0.49  # Backward-rewritten                   : 0
% 0.19/0.49  # Generated clauses                    : 13
% 0.19/0.49  # ...of the previous two non-redundant : 12
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 0
% 0.19/0.49  # Paramodulations                      : 13
% 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                  : 8
% 0.19/0.49  # ...of those cached                   : 5
% 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  : 18
% 0.19/0.49  #    Positive orientable unit clauses  : 5
% 0.19/0.49  #    Positive unorientable unit clauses: 0
% 0.19/0.49  #    Negative unit clauses             : 3
% 0.19/0.49  #    Non-unit-clauses                  : 10
% 0.19/0.49  # Current number of unprocessed clauses: 1
% 0.19/0.49  # ...number of literals in the above   : 4
% 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) : 73
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 23
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 3
% 0.19/0.49  # Unit Clause-clause subsumption calls : 11
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 0
% 0.19/0.49  # BW rewrite match successes           : 0
% 0.19/0.49  # Condensation attempts                : 29
% 0.19/0.49  # Condensation successes               : 2
% 0.19/0.49  # Termbank termtop insertions          : 2496
% 0.19/0.49  # Search garbage collected termcells   : 507
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.006 s
% 0.19/0.49  # System time              : 0.002 s
% 0.19/0.49  # Total time               : 0.008 s
% 0.19/0.49  # Maximum resident set size: 1896 pages
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.006 s
% 0.19/0.49  # System time              : 0.005 s
% 0.19/0.49  # Total time               : 0.011 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
%------------------------------------------------------------------------------