TSTP Solution File: SEU630^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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 03:28:42 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    :   30 (   8 unt;  12 typ;   0 def)
%            Number of atoms       :   64 (   9 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  263 (  15   ~;  12   |;  14   &; 201   @)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   70 (  12   ^  48   !;  10   ?;  70   :)

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

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

thf(decl_26,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

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

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

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

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

thf(decl_31,type,
    ubforcartprodlem3: $o ).

thf(decl_32,type,
    esk1_0: $i ).

thf(decl_33,type,
    esk2_0: $i ).

thf(decl_34,type,
    esk3_0: $i ).

thf(decl_35,type,
    esk4_0: $i ).

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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).

thf(cartprodpairin,conjecture,
    ( dsetconstrI
   => ( ubforcartprodlem3
     => ! [X1: $i,X5: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X5 )
             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X5 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).

thf(ubforcartprodlem3,axiom,
    ( ubforcartprodlem3
  <=> ! [X1: $i,X5: $i,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X5 )
           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).

thf(cartprod,axiom,
    ( cartprod
    = ( ^ [X1: $i,X5: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ X5 ) ) )
          @ ^ [X3: $i] :
            ? [X4: $i] :
              ( ( in @ X4 @ X1 )
              & ? [X6: $i] :
                  ( ( in @ X6 @ X5 )
                  & ( X3
                    = ( kpair @ X4 @ X6 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprod) ).

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,negated_conjecture,
    ~ ( ! [X18: $i,X19: $i > $o,X20: $i] :
          ( ( in @ X20 @ X18 )
         => ( ( X19 @ X20 )
           => ( in @ X20 @ ( dsetconstr @ X18 @ X19 ) ) ) )
     => ( ! [X21: $i,X22: $i,X23: $i] :
            ( ( in @ X23 @ X21 )
           => ! [X24: $i] :
                ( ( in @ X24 @ X22 )
               => ( in @ ( kpair @ X23 @ X24 ) @ ( powerset @ ( powerset @ ( binunion @ X21 @ X22 ) ) ) ) ) )
       => ! [X1: $i,X5: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X5 )
               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X5 ) ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cartprodpairin]),ubforcartprodlem3]),c_0_4])]) ).

thf(c_0_6,plain,
    ( cartprod
    = ( ^ [Z0: $i,Z1: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
          @ ^ [Z2: $i] :
            ? [X4: $i] :
              ( ( in @ X4 @ Z0 )
              & ? [X6: $i] :
                  ( ( in @ X6 @ Z1 )
                  & ( Z2
                    = ( kpair @ X4 @ X6 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cartprod]) ).

thf(c_0_7,negated_conjecture,
    ! [X25: $i,X26: $i > $o,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i] :
      ( ( ~ ( in @ X27 @ X25 )
        | ~ ( X26 @ X27 )
        | ( in @ X27 @ ( dsetconstr @ X25 @ X26 ) ) )
      & ( ~ ( in @ X30 @ X28 )
        | ~ ( in @ X31 @ X29 )
        | ( in @ ( kpair @ X30 @ X31 ) @ ( powerset @ ( powerset @ ( binunion @ X28 @ X29 ) ) ) ) )
      & ( in @ esk3_0 @ esk1_0 )
      & ( in @ esk4_0 @ esk2_0 )
      & ~ ( in @ ( kpair @ esk3_0 @ esk4_0 ) @ ( cartprod @ esk1_0 @ esk2_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_5])])])])]) ).

thf(c_0_8,plain,
    ( cartprod
    = ( ^ [Z0: $i,Z1: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
          @ ^ [Z2: $i] :
            ? [X49: $i] :
              ( ( in @ X49 @ Z0 )
              & ? [X50: $i] :
                  ( ( in @ X50 @ Z1 )
                  & ( Z2
                    = ( kpair @ X49 @ X50 ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,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_10,plain,
    ! [X1: $i,X3: $i] :
      ( ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ X3 ) ) )
        @ ^ [Z0: $i] :
          ? [X51: $i] :
            ( ( in @ X51 @ X1 )
            & ? [X52: $i] :
                ( ( in @ X52 @ X3 )
                & ( Z0
                  = ( kpair @ X51 @ X52 ) ) ) ) )
      = ( cartprod @ X1 @ X3 ) ),
    inference(arg_cong,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ( in @ X1 @ ( cartprod @ X3 @ X4 ) )
      | ~ ? [X53: $i] :
            ( ( in @ X53 @ X3 )
            & ? [X54: $i] :
                ( ( in @ X54 @ X4 )
                & ( X1
                  = ( kpair @ X53 @ X54 ) ) ) )
      | ~ ( in @ X1 @ ( powerset @ ( powerset @ ( binunion @ X3 @ X4 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i,X5: $i] :
      ( ( in @ ( kpair @ X1 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X3 @ X5 ) ) ) )
      | ~ ( in @ X1 @ X3 )
      | ~ ( in @ X4 @ X5 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_13,negated_conjecture,
    ~ ( in @ ( kpair @ esk3_0 @ esk4_0 ) @ ( cartprod @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i,X5: $i] :
      ( ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
      | ~ ( in @ X1 @ X4 )
      | ~ ( in @ X3 @ X5 ) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_11])]),c_0_12]) ).

thf(c_0_15,negated_conjecture,
    in @ esk3_0 @ esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_16,negated_conjecture,
    in @ esk4_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_17,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n008.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 16:06:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 0.19/0.49  # Version: 3.1.0-ho
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSFA.
% 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 full_lambda_3 with 300s (1) cores
% 0.19/0.49  # Starting ho_unfolding_6 with 300s (1) cores
% 0.19/0.49  # Starting sh4l with 300s (1) cores
% 0.19/0.49  # full_lambda_3 with pid 8669 completed with status 0
% 0.19/0.49  # Result found by full_lambda_3
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSFA.
% 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 full_lambda_3 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.19/0.49  # Search class: HHUSF-FFSS21-DSFFMSBN
% 0.19/0.49  # partial match(3): HHUSF-FFSF22-SSFFMSBN
% 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 8673 completed with status 0
% 0.19/0.49  # Result found by new_ho_10
% 0.19/0.49  # Preprocessing class: HSSSSLSSSLMNSFA.
% 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 full_lambda_3 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.19/0.49  # Search class: HHUSF-FFSS21-DSFFMSBN
% 0.19/0.49  # partial match(3): HHUSF-FFSF22-SSFFMSBN
% 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                        : 15
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 10
% 0.19/0.49  # Initial clauses                      : 7
% 0.19/0.49  # Removed in clause preprocessing      : 0
% 0.19/0.49  # Initial clauses in saturation        : 7
% 0.19/0.49  # Processed clauses                    : 21
% 0.19/0.49  # ...of these trivial                  : 0
% 0.19/0.49  # ...subsumed                          : 0
% 0.19/0.49  # ...remaining for further processing  : 21
% 0.19/0.49  # Other redundant clauses eliminated   : 1
% 0.19/0.49  # Clauses deleted for lack of memory   : 0
% 0.19/0.49  # Backward-subsumed                    : 0
% 0.19/0.49  # Backward-rewritten                   : 0
% 0.19/0.49  # Generated clauses                    : 12
% 0.19/0.49  # ...of the previous two non-redundant : 7
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 1
% 0.19/0.49  # Paramodulations                      : 4
% 0.19/0.49  # Factorizations                       : 0
% 0.19/0.49  # NegExts                              : 0
% 0.19/0.49  # Equation resolutions                 : 1
% 0.19/0.49  # Disequality decompositions           : 0
% 0.19/0.49  # Total rewrite steps                  : 6
% 0.19/0.49  # ...of those cached                   : 0
% 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  : 13
% 0.19/0.49  #    Positive orientable unit clauses  : 9
% 0.19/0.49  #    Positive unorientable unit clauses: 0
% 0.19/0.49  #    Negative unit clauses             : 1
% 0.19/0.49  #    Non-unit-clauses                  : 3
% 0.19/0.49  # Current number of unprocessed clauses: 0
% 0.19/0.49  # ...number of literals in the above   : 0
% 0.19/0.49  # Current number of archived formulas  : 0
% 0.19/0.49  # Current number of archived clauses   : 8
% 0.19/0.49  # Clause-clause subsumption calls (NU) : 6
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 5
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 1
% 0.19/0.49  # Unit Clause-clause subsumption calls : 1
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 2
% 0.19/0.49  # BW rewrite match successes           : 0
% 0.19/0.49  # Condensation attempts                : 21
% 0.19/0.49  # Condensation successes               : 0
% 0.19/0.49  # Termbank termtop insertions          : 1588
% 0.19/0.49  # Search garbage collected termcells   : 299
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.002 s
% 0.19/0.49  # System time              : 0.004 s
% 0.19/0.49  # Total time               : 0.007 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                : 0.004 s
% 0.19/0.49  # System time              : 0.007 s
% 0.19/0.49  # Total time               : 0.010 s
% 0.19/0.49  # Maximum resident set size: 1712 pages
% 0.19/0.49  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------